GAP (ref) - References

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[SPAS] SPAS - Subgroup Presentation Algorithms System, version 2.5, User's reference manual, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1989).

[AMW82] Arrell, D. G., Manrai, S. and Worboys, M. F. (Campbell, C. M. and Robertson, E. F., Eds.), A procedure for obtaining simplified defining relations for a subgroup, in Groups–St Andrews 1981 (St Andrews, 1981), Cambridge Univ. Press, London Math. Soc. Lecture Note Ser., 71, Cambridge (1982), 155–159.

[AR84] Arrell, D. G. and Robertson, E. F. (Atkinson, M. D., Ed.), A modified Todd-Coxeter algorithm, in Computational group theory (Durham, 1982), Academic Press, London (1984), 27–32.

[Art73] Artin, E., Galoissche Theorie, Verlag Harri Deutsch, Zurich (1973), 86 pages
(Übersetzung nach der zweiten englischen Auflage besorgt von Viktor Ziegler, Mit einem Anhang von N. A. Milgram, Zweite, unveränderte Auflage, Deutsch-Taschenbücher, No. 21).

[BCFS91] Babai, L., Cooperman, G., Finkelstein, L. and Seress, Á., Nearly Linear Time Algorithms for Permutation Groups with a Small Base, in Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC'91), Bonn 1991, ACM Press (1991), 200–209.

[Bak84] Baker, A., A concise introduction to the theory of numbers, Cambridge University Press, Cambridge (1984), xiii+95 pages.

[BC94] Baum, U. and Clausen, M., Computing irreducible representations of supersolvable groups, Math. Comp., 63 (207) (1994), 351–359.

[BTW93] Beauzamy, B., Trevisan, V. and Wang, P. S., Polynomial factorization: sharp bounds, efficient algorithms, J. Symbolic Comput., 15 (4) (1993), 393–413.

[BC76] Beetham, M. J. and Campbell, C. M., A note on the Todd-Coxeter coset enumeration algorithm, Proc. Edinburgh Math. Soc. (2), 20 (1) (1976), 73–79.

[Ber76] Berger, T. R., Characters and derived length in groups of odd order, J. Algebra, 39 (1) (1976), 199–207.

[Bes92] Besche, H. U., Die Berechnung von Charaktergraden und Charakteren endlicher auflösbarer Gruppen im Computeralgebrasystem GAP, Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1992).

[BE99a] Besche, H. U. and Eick, B., Construction of finite groups, J. Symbolic Comput., 27 (4) (1999), 387–404.

[BE99b] Besche, H. U. and Eick, B., The groups of order at most 1000 except 512 and 768, J. Symbolic Comput., 27 (4) (1999), 405–413.

[BE01] Besche, H. U. and Eick, B., The groups of order q^n ⋅ p, Comm. Algebra, 29 (4) (2001), 1759–1772.

[BEO01] Besche, H. U., Eick, B. and O'Brien, E. A., The groups of order at most 2000, Electron. Res. Announc. Amer. Math. Soc., 7 (2001), 1–4 (electronic).

[BEO02] Besche, H. U., Eick, B. and O'Brien, E. A., A millennium project: constructing small groups, Internat. J. Algebra Comput., 12 (5) (2002), 623–644.

[BFS79] Beyl, F. R., Felgner, U. and Schmid, P., On groups occurring as center factor groups, J. Algebra, 61 (1) (1979), 161–177.

[Bou70] Bourbaki, N., Éléments de mathématique. Algèbre. Chapitres 1 à 3, Hermann, Paris (1970), xiii+635 pp. (not consecutively paged) pages.

[BC89] Brent, R. P. and Cohen, G. L., A new lower bound for odd perfect numbers, Math. Comp., 53 (187) (1989), 431–437, S7–S24.

[Bre91] Breuer, T., Potenzabbildungen, Untergruppenfusionen, Tafel-Automorphismen, Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1991).

[Bre97] Breuer, T., Integral bases for subfields of cyclotomic fields, Appl. Algebra Engrg. Comm. Comput., 8 (4) (1997), 279–289.

[Bre99] Breuer, T., Computing possible class fusions from character tables, Comm. Algebra, 27 (6) (1999), 2733–2748.

[BL98] Breuer, T. and Linton, S., The GAP 4 Type System. Organizing Algebraic Algorithms, in ISSAC '98: Proceedings of the 1998 international symposium on Symbolic and algebraic computation, ACM Press, New York, NY, USA (1998), 38–45
(Chairman: Volker Weispfenning and Barry Trager).

[BP98] Breuer, T. and Pfeiffer, G., Finding possible permutation characters, J. Symbolic Comput., 26 (3) (1998), 343–354.

[BLS75] Brillhart, J., Lehmer, D. and Selfridge, J., New primality criteria and factorizations of 2^m ± 1, Mathematics of Computation, 29 (1975), 620–647.

[BJR87] Brown, R., Johnson, D. L. and Robertson, E. F., Some computations of nonabelian tensor products of groups, J. Algebra, 111 (1) (1987), 177–202.

[Bur55] Burnside, W., Theory of groups of finite order, Dover Publications Inc., New York (1955), xxiv+512 pages
(Unabridged republication of the second edition, published in 1911).

[But93] Butler, G., The transitive groups of degree fourteen and fifteen, J. Symbolic Comput., 16 (5) (1993), 413–422.

[BM83] Butler, G. and McKay, J., The transitive groups of degree up to eleven, Comm. Algebra, 11 (8) (1983), 863–911.

[Can73] Cannon, J. J., Construction of defining relators for finite groups, Discrete Math., 5 (1973), 105–129.

[Car72] Carter, R. W., Simple groups of Lie type, John Wiley & Sons, London-New York-Sydney (1972), viii+331 pages
(Pure and Applied Mathematics, Vol. 28).

[Coh93] Cohen, H., A course in computational algebraic number theory, Springer-Verlag, Graduate Texts in Mathematics, 138, Berlin (1993), xii+534 pages.

[Con90a] Conlon, S. B., Calculating characters of p-groups, J. Symbolic Comput., 9 (5-6) (1990), 535–550
(Computational group theory, Part 1).

[Con90b] Conlon, S. B., Computing modular and projective character degrees of soluble groups, J. Symbolic Comput., 9 (5-6) (1990), 551–570
(Computational group theory, Part 1).

[CCNPW85] Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of finite groups, Oxford University Press, Eynsham (1985), xxxiv+252 pages
(Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray).

[CHM98] Conway, J. H., Hulpke, A. and McKay, J., On transitive permutation groups, LMS J. Comput. Math., 1 (1998), 1–8 (electronic).

[CLO97] Cox, D., Little, J. and O'Shea, D., Ideals, varieties, and algorithms, Springer-Verlag, Second edition, Undergraduate Texts in Mathematics, New York (1997), xiv+536 pages
(An introduction to computational algebraic geometry and commutative algebra).

[DE05] Dietrich, H. and Eick, B., On the groups of cube-free order, J. Algebra, 292 (1) (2005), 122–137.

[Dix67] Dixon, J. D., High speed computation of group characters, Numer. Math., 10 (1967), 446–450.

[Dix93] Dixon, J. D. (Finkelstein, L. and Kantor, W. M., Eds.), Constructing representations of finite groups, in Groups and computation (New Brunswick, NJ, 1991), Amer. Math. Soc., DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 11, Providence, RI (1993), 105–112.

[DM88] Dixon, J. D. and Mortimer, B., The primitive permutation groups of degree less than 1000, Math. Proc. Cambridge Philos. Soc., 103 (2) (1988), 213–238.

[Dre69] Dress, A., A characterisation of solvable groups, Math. Z., 110 (1969), 213–217.

[Eic97] Eick, B. (Finkelstein, L. and Kantor, W. M., Eds.), Special presentations for finite soluble groups and computing (pre-)Frattini subgroups, in Groups and computation, II (New Brunswick, NJ, 1995), Amer. Math. Soc., DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 28, Providence, RI (1997), 101–112.

[EH03] Eick, B. and Höfling, B., The solvable primitive permutation groups of degree at most 6560, LMS J. Comput. Math., 6 (2003), 29–39 (electronic).

[EH] Eick, B. and Hulpke, A., Computing the maximal subgroups of a permutation group I, 155–168.

[EO99a] Eick, B. and O'Brien, E. A., Enumerating p-groups, J. Austral. Math. Soc. Ser. A, 67 (2) (1999), 191–205
(Group theory).

[EO99b] Eick, B. and O'Brien, E. A. (Matzat, B. H., Greuel, G.-M. and Hiss, G., Eds.), The groups of order 512, in Algorithmic algebra and number theory (Heidelberg, 1997), Springer, Berlin (1999), 379–380
(Proceedings of Abschlusstagung des DFG Schwerpunktes Algorithmische Algebra und Zahlentheorie in Heidelberg).

[Ell98] Ellis, G., On the capability of groups, Proc. Edinburgh Math. Soc. (2), 41 (3) (1998), 487–495.

[FJNT95] Felsch, V., Johnson, D. L., Neubüser, J. and Tsaranov, S. V., The structure of certain Coxeter groups, in Groups '93 Galway/St Andrews, Vol. 1 (Galway, 1993), Cambridge Univ. Press, London Math. Soc. Lecture Note Ser., 211, Cambridge (1995), 177–190.

[FN79] Felsch, V. and Neubüser, J. (Ng, E. W., Ed.), An algorithm for the computation of conjugacy classes and centralizers in p-groups, in Symbolic and algebraic computation (EUROSAM '79, Internat. Sympos., Marseille, 1979), Springer, Lecture Notes in Comput. Sci., 72, Berlin (1979), 452–465
(EUROSAM '79, an International Symposium held in Marseille, June 1979).

[Fra82] Frame, J. S., Recursive computation of tensor power components, Bayreuth. Math. Schr., 10 (1982), 153–159.

[Gir03] Girnat, B., Klassifikation der Gruppen bis zur Ordnung p^5, Staatsexamensarbeit, TU Braunschweig, Braunschweig, Germany (2003).

[Hal36] Hall, P., The Eulerian functions of a group, Quarterly J. Of Mathematics, os-7 (1) (1936), 134–151.

[HJ59] Hall Jr., M., The theory of groups, The Macmillan Co., New York, N.Y. (1959), xiii+434 pages.

[Hav69] Havas, G., Symbolic and Algebraic Calculation, Basser Computing Dept., Technical Report, Basser Department of Computer Science, University of Sydney (89), Sydney, Australia (1969).

[HKRR84] Havas, G., Kenne, P. E., Richardson, J. S. and Robertson, E. F. (Atkinson, M. D., Ed.), A Tietze transformation program, in Computational group theory (Durham, 1982), Academic Press, London (1984), 69–73.

[Hav74] Havas, G. (Newman, M. F., Ed.), A Reidemeister-Schreier program, in Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973), Springer, Lecture Notes in Math., 372, Berlin (1974), 347–356. Lecture Notes in Math., Vol. 372
(Held at the Australian National University, Canberra, August 13–24, 1973, With an introduction by B. H. Neumann, Lecture Notes in Mathematics, Vol. 372).

[HIÖ89] Hawkes, T., Isaacs, I. M. and Özaydin, M., On the Möbius function of a finite group, Rocky Mountain J. Math., 19 (4) (1989), 1003–1034.

[HJLP] Hiss, G., Jansen, C., Lux, K. and Parker, R. A., Computational Modular Character Theory, http://www.math.rwth-aachen.de/~MOC/CoMoChaT/.

[HP89] Holt, D. F. and Plesken, W., Perfect groups, The Clarendon Press Oxford University Press, Oxford Mathematical Monographs, New York (1989), xii+364 pages
(With an appendix by W. Hanrath, Oxford Science Publications).

[HR94] Holt, D. F. and Rees, S., Testing modules for irreducibility, J. Austral. Math. Soc. Ser. A, 57 (1) (1994), 1–16.

[How76] Howie, J. M., An introduction to semigroup theory, Academic Press [Harcourt Brace Jovanovich Publishers], London (1976), x+272 pages
(L.M.S. Monographs, No. 7).

[Hul93] Hulpke, A., Zur Berechnung von Charaktertafeln, Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule (1993).

[Hul96] Hulpke, A., Konstruktion transitiver Permutationsgruppen, Dissertation, Verlag der Augustinus Buchhandlung, Aachen, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1996).

[Hul98] Hulpke, A., Computing normal subgroups, in Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation (Rostock), ACM, New York (1998), 194–198 (electronic)
(Chairman: Volker Weispfenning and Barry Trager).

[Hul99] Hulpke, A., Computing subgroups invariant under a set of automorphisms, J. Symbolic Comput., 27 (4) (1999), 415–427.

[Hul00] Hulpke, A., Conjugacy classes in finite permutation groups via homomorphic images, Math. Comp., 69 (232) (2000), 1633–1651.

[Hul01] Hulpke, A., Representing subgroups of finitely presented groups by quotient subgroups, Experiment. Math., 10 (3) (2001), 369–381.

[Hul05] Hulpke, A., Constructing transitive permutation groups, J. Symbolic Comput., 39 (1) (2005), 1–30.

[Hum72] Humphreys, J. E., Introduction to Lie algebras and representation theory, Springer-Verlag, New York (1972), xii+169 pages
(Graduate Texts in Mathematics, Vol. 9).

[Hum78] Humphreys, J. E., Introduction to Lie algebras and representation theory, Springer-Verlag, Graduate Texts in Mathematics, 9, New York (1978), xii+171 pages
(Second printing, revised).

[Hup67] Huppert, B., Endliche Gruppen. I, Springer-Verlag, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Berlin (1967), xii+793 pages.

[HB82] Huppert, B. and Blackburn, N., Finite groups. II, Springer-Verlag, Grundlehren Math. Wiss., 242, Berlin (1982), xiii+531 pages.

[Isa76] Isaacs, I. M., Character theory of finite groups, Academic Press [Harcourt Brace Jovanovich Publishers], New York (1976), xii+303 pages
(Pure and Applied Mathematics, No. 69).

[IE94] Ishibashi, H. and Earnest, A. G., Two-element generation of orthogonal groups over finite fields, J. Algebra, 165 (1) (1994), 164–171.

[JLPW95] Jansen, C., Lux, K., Parker, R. and Wilson, R., An atlas of Brauer characters, The Clarendon Press Oxford University Press, London Mathematical Society Monographs. New Series, 11, New York (1995), xviii+327 pages
(Appendix 2 by T. Breuer and S. Norton, Oxford Science Publications).

[Joh97] Johnson, D. L., Presentations of groups, Cambridge University Press, Second edition, London Mathematical Society Student Texts, 15, Cambridge (1997), xii+216 pages.

[Kau92] Kaup, A., Gitterbasen und Charaktere endlicher Gruppen, Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1992).

[KLM01] Kemper, G., Lübeck, F. and Magaard, K., Matrix generators for the Ree groups ^2G_2(q), Comm. Algebra, 29 (1) (2001), 407–413.

[KL90] Kleidman, P. and Liebeck, M., The subgroup structure of the finite classical groups, Cambridge University Press, London Mathematical Society Lecture Note Series, 129, Cambridge (1990), x+303 pages.

[Kli66] Klimyk, A. U., Decomposition of the direct product of irreducible representations of semisimple Lie algebras into irreducible representations, Ukrain. Mat. Ž., 18 (5) (1966), 19–27.

[Kli68] Klimyk, A. U., Decomposition of a direct product of irreducible representations of a semisimple Lie algebra into irreducible representations, in American Mathematical Society Translations. Series 2, American Mathematical Society, 76, Providence, R.I. (1968), 63–73.

[Knu98] Knuth, D. E., The Art of Computer Programming, Volume 2: Seminumerical Algorithms, Addison-Wesley, third edition (1998).

[LNS84] Laue, R., Neubüser, J. and Schoenwaelder, U. (Atkinson, M. D., Ed.), Algorithms for finite soluble groups and the SOGOS system, in Computational group theory (Durham, 1982), Academic Press, London (1984), 105–135.

[LLL82] Lenstra, A. K., Lenstra Jr., H. W. and Lovász, L., Factoring polynomials with rational coefficients, Math. Ann., 261 (4) (1982), 515–534.

[Leo91] Leon, J. S., Permutation group algorithms based on partitions. I. Theory and algorithms, J. Symbolic Comput., 12 (4-5) (1991), 533–583
(Computational group theory, Part 2).

[Lüb03] Lübeck, F., Conway polynomials for finite fields (2003), http://www.math.rwth-aachen.de:8001/~Frank.Luebeck/data/ConwayPol.

[LRW97] Luks, E. M., Rákóczi, F. and Wright, C. R. B., Some algorithms for nilpotent permutation groups, J. Symbolic Comput., 23 (4) (1997), 335–354.

[LP91] Lux, K. and Pahlings, H. (Michler, G. O. and Ringel, C. M., Eds.), Computational aspects of representation theory of finite groups, in Representation theory of finite groups and finite-dimensional algebras (Bielefeld, 1991), Birkhäuser, Progr. Math., 95, Basel (1991), 37–64.

[Maa10] Maas, L., On a construction of the basic spin representations of symmetric groups, Communications in Algebra, 38 (2010), 4545–4552.

[Mac81] Macdonald, I. G., Numbers of conjugacy classes in some finite classical groups, Bull. Austral. Math. Soc., 23 (1) (1981), 23–48.

[MV97] Mahajan, M. and Vinay, V., Determinant: combinatorics, algorithms, and complexity, Chicago J. Theoret. Comput. Sci. (1997), Article 5, 26 pp. (electronic).

[MY79] McKay, J. and Young, K. C., The nonabelian simple groups G, |G| < 10^6–minimal generating pairs, Math. Comp., 33 (146) (1979), 812–814.

[MN89] Mecky, M. and Neubüser, J., Some remarks on the computation of conjugacy classes of soluble groups, Bull. Austral. Math. Soc., 40 (2) (1989), 281–292.

[Mur58] Murnaghan, F. D., The orthogonal and symplectic groups, Comm. Dublin Inst. Adv. Studies. Ser. A, no., 13 (1958), 146.

[Neb95] Nebe, G., Endliche rationale Matrixgruppen vom Grad 24, Dissertation, Rheinisch Westfälische Technische Hochschule, Aachener Beiträge zur Mathematik, 12, Aachen, Germany (1995).

[Neb96] Nebe, G., Finite subgroups of GL_n(Q) for 25 ≤ n ≤ 31, Comm. Algebra, 24 (7) (1996), 2341–2397.

[NP95] Nebe, G. and Plesken, W., Finite rational matrix groups of degree 16, Mem. Amer. Math. Soc., AMS (556) (1995), 74–144
(vol. 116).

[Neu82] Neubüser, J. (Campbell, C. M. and Robertson, E. F., Eds.), An elementary introduction to coset table methods in computational group theory, in Groups–St Andrews 1981 (St Andrews, 1981), Cambridge Univ. Press, London Math. Soc. Lecture Note Ser., 71, Cambridge (1982), 1–45.

[NPP84] Neubüser, J., Pahlings, H. and Plesken, W. (Atkinson, M. D., Ed.), CAS; design and use of a system for the handling of characters of finite groups, in Computational group theory (Durham, 1982), Academic Press, London (1984), 195–247.

[Neu92] Neukirch, J., Algebraische Zahlentheorie, Springer, Berlin, Heidelberg and New York (1992).

[New90] Newman, M. F., Proving a group infinite, Arch. Math. (Basel), 54 (3) (1990), 209–211.

[New77] Newman, M. F. (Bryce, R. A., Cossey, J. and Newman, M. F., Eds.), Determination of groups of prime-power order, in Group theory (Proc. Miniconf., Australian Nat. Univ., Canberra, 1975), Springer, Lecture Notes in Math., 573, Berlin (1977), 73–84. Lecture Notes in Math., Vol. 573
(Lecture Notes in Mathematics, Vol. 573).

[NOV04] Newman, M. F., O'Brien, E. A. and Vaughan-Lee, M. R., Groups and nilpotent Lie rings whose order is the sixth power of a prime, J. Algebra, 278 (1) (2004), 383–401.

[O'B90] O'Brien, E. A., The p-group generation algorithm, J. Symbolic Comput., 9 (5-6) (1990), 677–698
(Computational group theory, Part 1).

[O'B91] O'Brien, E. A., The groups of order 256, J. Algebra, 143 (1) (1991), 219–235.

[OV05] O'Brien, E. A. and Vaughan-Lee, M. R., The groups with order p^7 for odd prime p, J. Algebra, 292 (1) (2005), 243–258.

[Pah93] Pahlings, H., On the Möbius function of a finite group, Arch. Math. (Basel), 60 (1) (1993), 7–14.

[Par84] Parker, R. A. (Atkinson, M. D., Ed.), The computer calculation of modular characters (the meat-axe), in Computational group theory (Durham, 1982), Academic Press, London (1984), 267–274.

[Pfe91] Pfeiffer, G., Von Permutationscharakteren und Markentafeln, Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1991).

[Pfe97] Pfeiffer, G., The subgroups of M_24, or how to compute the table of marks of a finite group, Experiment. Math., 6 (3) (1997), 247–270.

[Ple85] Plesken, W., Finite unimodular groups of prime degree and circulants, J. Algebra, 97 (1) (1985), 286–312.

[Ple95] Plesken, W., Solving XX^ tr = A over the integers, Linear Algebra Appl., 226/228 (1995), 331--344.

[PN95] Plesken, W. and Nebe, G., Finite rational matrix groups, Mem. Amer. Math. Soc., AMS (556) (1995), 1–73
(vol. 116).

[PP77] Plesken, W. and Pohst, M., On maximal finite irreducible Subgroups of GL(n,Z). I. The five and seven dimensional cases, II. The six dimensional case, Math. Comp., 31 (1977), 536–576.

[PP80] Plesken, W. and Pohst, M., On maximal finite irreducible Subgroups of GL(n,Z). III. The nine dimensional case, IV. Remarks on even dimensions with application to n = 8, V. The eight dimensional case and a complete description of dimensions less than ten, Math. Comp., 34 (1980), 245–301.

[Poh87] Pohst, M., A modification of the LLL reduction algorithm, J. Symbolic Comput., 4 (1) (1987), 123–127.

[Rin93] Ringe, M., The C MeatAxe, Release 1.5, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1993).

[Rob88] Robertson, E. F., Tietze transformations with weighted substring search, J. Symbolic Comput., 6 (1) (1988), 59–64.

[Ron05] Roney-Dougal, C. M., The primitive permutation groups of degree less than 2500, J. Algebra, 292 (1) (2005), 154–183.

[RU03] Roney-Dougal, C. M. and Unger, W. R., The affine primitive permutation groups of degree less than 1000, J. Symbolic Comput., 35 (4) (2003), 421–439.

[Roy87] Royle, G. F., The transitive groups of degree twelve, J. Symbolic Comput., 4 (2) (1987), 255–268.

[RT98] Rylands, L. J. and Taylor, D. E., Matrix generators for the orthogonal groups, J. Symbolic Comput., 25 (3) (1998), 351–360.

[Sch92] Scherner, M., Erweiterung einer Arithmetik von Kreisteilungskörpern auf deren Teilkörper und deren Implementation in GAP, Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1992).

[Sch94] Schiffer, U., Cliffordmatrizen, Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1994).

[Sch90] Schneider, G. J. A., Dixon's character table algorithm revisited, J. Symbolic Comput., 9 (5-6) (1990), 601–606
(Computational group theory, Part 1).

[Sch11] Schur, J., Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen, Journal für die reine und angewandte Mathematik, 139 (1911), 155–250.

[Sco73] Scott, L. L., Modular permutation representations, Trans. Amer. Math. Soc., 175 (1973), 101–121.

[Ser03] Seress, Á., Permutation Group Algorithms, Cambridge University Press (2003).

[Sho92] Short, M. W., The primitive soluble permutation groups of degree less than 256, Springer-Verlag, Lecture Notes in Mathematics, 1519, Berlin (1992), x+145 pages.

[Sim90] Sims, C. C., Computing the order of a solvable permutation group, J. Symbolic Comput., 9 (5-6) (1990), 699–705
(Computational group theory, Part 1).

[Sim94] Sims, C. C., Computation with finitely presented groups, Cambridge University Press, Encyclopedia of Mathematics and its Applications, 48, Cambridge (1994), xiii+604 pages.

[ACM] Sims, C. C. (Küchlin, W., Ed.), Computing with subgroups of automorphism groups of finite groups, in Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), The Association for Computing Machinery, ACM, New York (1997), 400–403 (electronic)
(Held in Kihei, HI, July 21–23, 1997).

[Sim70] Sims, C. C. (Leech, J., Ed.), Computational methods in the study of permutation groups, in Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) , Pergamon, Proceedings of a Conference held at Oxford under the auspices of the Science Research Council, Atlas Computer Laboratory, 29, Oxford (1970), 169–183
(RUSSIAN translation in: Computations in algebra and number theory (Russian), edited by B. B. Venkov and D. K. Faddeev, pp. 129–147, Matematika, Novoie v Zarubeznoi Naukie, vol. 2, Izdat. MIR, Moscow, 1976).

[SM85] Soicher, L. and McKay, J., Computing Galois groups over the rationals, J. Number Theory, 20 (3) (1985), 273–281.

[Sou94] Souvignier, B., Irreducible finite integral matrix groups of degree 8 and 10, Math. Comp., 63 (207) (1994), 335–350
(With microfiche supplement).

[Tay87] Taylor, D. E., Pairs of Generators for Matrix Groups. I, The Cayley Bulletin, 3 (1987).

[The93] Theißen, H., Methoden zur Bestimmung der rationalen Konjugiertheit in endlichen Gruppen, Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1993).

[The97] Theißen, H., Eine Methode zur Normalisatorberechnung in Permutationsgruppen mit Anwendungen in der Konstruktion primitiver Gruppen, Dissertation, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1997).

[vdW76] van der Waall, R. W., On symplectic primitive modules and monomial groups, Nederl. Akad. Wetensch. Proc. Ser. A 79, Indag. Math., 38 (4) (1976), 362–375.

[Wag90] Wagon, S., Editor's corner: the Euclidean algorithm strikes again, Amer. Math. Monthly, 97 (2) (1990), 125–129.

[Wie69] Wielandt, H., Permutation groups through invariant relations and invariant functions, Lecture Notes, Department of Mathematics, The Ohio State University (1969).

[Zag90] Zagier, D., A one-sentence proof that every prime p ≡ 1 mod 4 is a sum of two squares, Amer. Math. Monthly, 97 (2) (1990), 144.

[Zum89] Zumbroich, M., Grundlagen einer Arithmetik in Kreisteilungskörpern und ihre Implementation in CAS, Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1989).

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