  
  
                                    [1X recog [101X
  
  
                  [1X A collection of group recognition methods [101X
  
  
                                     1.3.2
  
  
                                 15 April 2018
  
  
                                 Max Neunhöffer
  
                                  Ákos Seress
  
                             Nurullah Ankaralioglu
  
                                Peter Brooksbank
  
                                  Frank Celler
  
                                  Stephen Howe
  
                                   Maska Law
  
                                  Steve Linton
  
                                  Gunter Malle
  
                                 Alice Niemeyer
  
                                 Eamonn O'Brien
  
                             Colva M. Roney-Dougal
  
                                    Max Horn
  
  
  
  Max Neunhöffer
      Email:    [7Xmailto:max@9hoeffer.de[107X
      Homepage: [7Xhttp://www-groups.mcs.st-and.ac.uk/~neunhoef[107X
      Address:  [33X[0;14YGustav-Freytag-Straße 40[133X
                [33X[0;14Y50354 Hürth[133X
                [33X[0;14YGermany[133X
  
  
  Nurullah Ankaralioglu
      Email:    [7Xmailto:ankarali@atauni.edu.tr[107X
  Peter Brooksbank
      Email:    [7Xmailto:pbrooksb@bucknell.edu[107X
      Homepage: [7Xhttp://www.facstaff.bucknell.edu/pbrooksb/[107X
      Address:  [33X[0;14YPeter A. Brooksbank[133X
                [33X[0;14YMathematics Department[133X
                [33X[0;14YBucknell University[133X
                [33X[0;14YLewisburg, PA 17837[133X
                [33X[0;14YUSA[133X
  
  
  Frank Celler
      Email:    [7Xmailto:frank@celler.de[107X
      Homepage: [7Xhttp://www.celler.de/[107X
  Maska Law
      Email:    [7Xmailto:maska@maths.uwa.edu.au[107X
      Address:  [33X[0;14YMaska Law[133X
                [33X[0;14YUniversity of Western Australia[133X
                [33X[0;14YSchool of Mathematics and Statistics[133X
                [33X[0;14Y35 Stirling Highway[133X
                [33X[0;14YCrawley 6009[133X
                [33X[0;14YWestern Australia[133X
  
  
  Steve Linton
      Email:    [7Xmailto:sal@cs.st-andrews.ac.uk[107X
      Homepage: [7Xhttp://www-circa.mcs.st-and.ac.uk/~sal/[107X
      Address:  [33X[0;14YSchool of Computer Science[133X
                [33X[0;14YJack Cole Building[133X
                [33X[0;14YNorth Haugh[133X
                [33X[0;14YSt Andrews, Fife KY16 9SX[133X
                [33X[0;14YScotland, UK[133X
  
  
  Gunter Malle
      Email:    [7Xmailto:malle@mathematik.uni-kl.de[107X
      Homepage: [7Xhttp://www.mathematik.uni-kl.de/~malle/[107X
  Alice Niemeyer
      Email:    [7Xmailto:alice@maths.uwa.edu.au[107X
      Homepage: [7Xhttp://www.maths.uwa.edu.au/~alice/[107X
      Address:  [33X[0;14YAlice C. Niemeyer[133X
                [33X[0;14YUniversity of Western Australia[133X
                [33X[0;14YSchool of Mathematics and Statistics[133X
                [33X[0;14Y35 Stirling Highway[133X
                [33X[0;14YCrawley 6009[133X
                [33X[0;14YWestern Australia[133X
  
  
  Eamonn O'Brien
      Email:    [7Xmailto:obrien@math.auckland.ac.nz[107X
      Homepage: [7Xhttp://www.math.auckland.ac.nz/~obrien/[107X
  Colva M. Roney-Dougal
      Email:    [7Xmailto:colva@mcs.st-and.ac.uk[107X
      Homepage: [7Xhttp://www-groups.mcs.st-and.ac.uk/~colva[107X
      Address:  [33X[0;14YSchool of Mathematics and Statistics[133X
                [33X[0;14YMathematical Institute[133X
                [33X[0;14YNorth Haugh[133X
                [33X[0;14YSt Andrews, Fife KY16 9SS[133X
                [33X[0;14YScotland, UK[133X
  
  
  Max Horn
      Email:    [7Xmailto:max.horn@uni-siegen.de[107X
      Homepage: [7Xhttps://www.quendi.de/math[107X
      Address:  [33X[0;14YDepartment Mathematik[133X
                [33X[0;14YUniversität Siegen[133X
                [33X[0;14YWalter-Flex-Straße 3[133X
                [33X[0;14Y57072 Siegen[133X
                [33X[0;14YGermany[133X
  
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2005-2014 by Max Neunhöffer and Ákos Seress[133X
  
  [33X[0;0YThis  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 3 or (at your option) any later version.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (recog)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YPhilosophy[133X
    1.2 [33X[0;0YOverview over this manual[133X
    1.3 [33X[0;0YFeedback[133X
  2 [33X[0;0YInstallation of the [5Xrecog[105X-Package[133X
  3 [33X[0;0YGroup Recognition[133X
    3.1 [33X[0;0YThe recursive procedure[133X
      3.1-1 RecogniseGeneric
      3.1-2 RecognisePermGroup
      3.1-3 RecogniseMatrixGroup
      3.1-4 RecogniseProjectiveGroup
      3.1-5 RecogniseGroup
      3.1-6 FindHomDbPerm
      3.1-7 FindHomMethodsPerm
      3.1-8 SLPforElementFuncsPerm
      3.1-9 FindHomDbMatrix
      3.1-10 FindHomMethodsMatrix
      3.1-11 SLPforElementFuncsMatrix
      3.1-12 FindHomDbProjective
      3.1-13 FindHomMethodsProjective
      3.1-14 SLPforElementFuncsProjective
      3.1-15 TryFindHomMethod
    3.2 [33X[0;0YRecognition info records[133X
      3.2-1 RecognitionInfoFamily
      3.2-2 IsRecognitionInfo
      3.2-3 IsLeaf
      3.2-4 IsReady
      3.2-5 Grp
      3.2-6 Homom
      3.2-7 NiceGens
      3.2-8 pregensfac
      3.2-9 RIFac
      3.2-10 RIKer
      3.2-11 RIParent
      3.2-12 fhmethsel
      3.2-13 slpforelement
      3.2-14 SLPforElement
      3.2-15 StdPresentation
      3.2-16 methodsforfactor
      3.2-17 calcnicegens
      3.2-18 CalcNiceGensGeneric
      3.2-19 CalcNiceGensHomNode
      3.2-20 CalcNiceGens
      3.2-21 slptonice
      3.2-22 gensN
      3.2-23 findgensNmeth
      3.2-24 FindKernelRandom
      3.2-25 FindKernelDoNothing
      3.2-26 FindKernelFastNormalClosure
      3.2-27 gensNslp
      3.2-28 immediateverification
      3.2-29 forkernel
      3.2-30 forfactor
      3.2-31 isone
      3.2-32 isequal
      3.2-33 [33X[0;0YOther components of recognition info records[133X
    3.3 [33X[0;0YMethods to find homomorphisms[133X
      3.3-1 FindHomomorphism
      3.3-2 SLPforElementGeneric
    3.4 [33X[0;0YConventions for the recognition of permutation groups[133X
    3.5 [33X[0;0YConventions for the recognition of matrix groups[133X
    3.6 [33X[0;0YConventions for the recognition of projective groups[133X
  4 [33X[0;0YMethod Selection[133X
    4.1 [33X[0;0YWhat are methods?[133X
      4.1-1 AddMethod
    4.2 [33X[0;0YHow methods are called[133X
      4.2-1 CallMethods
  5 [33X[0;0YAfter successful recognition[133X
    5.1 [33X[0;0YFunctions and methods for recognition info records[133X
      5.1-1 SLPforNiceGens
      5.1-2 \in
      5.1-3 Size
      5.1-4 DisplayCompositionFactors
  6 [33X[0;0YMethods for recognition[133X
    6.1 [33X[0;0YMethods for permutation groups[133X
      6.1-1 [33X[0;0Y[10XTrivialPermGroup[110X[133X
      6.1-2 [33X[0;0Y[10XThrowAwayFixedPoints[110X[133X
      6.1-3 [33X[0;0Y[10XPcgs[110X[133X
      6.1-4 [33X[0;0Y[10XVeryFewPoints[110X[133X
      6.1-5 [33X[0;0Y[10XNontransitive[110X[133X
      6.1-6 [33X[0;0Y[10XGiant[110X[133X
      6.1-7 [33X[0;0Y[10XImprimitive[110X[133X
      6.1-8 [33X[0;0Y[10XSnkSetswrSr[110X[133X
      6.1-9 [33X[0;0Y[10XStabChain[110X[133X
    6.2 [33X[0;0YMethods for matrix groups[133X
      6.2-1 [33X[0;0Y[10XTrivialMatrixGroup[110X[133X
      6.2-2 [33X[0;0Y[10XKnownStabilizerChain[110X[133X
      6.2-3 [33X[0;0Y[10XDiagonalMatrices[110X[133X
      6.2-4 [33X[0;0Y[10XFewGensAbelian[110X[133X
      6.2-5 [33X[0;0Y[10XReducibleIso[110X[133X
      6.2-6 [33X[0;0Y[10XBlockLowerTriangular[110X[133X
      6.2-7 [33X[0;0Y[10XBlockDiagonal[110X[133X
      6.2-8 [33X[0;0Y[10XGoProjective[110X[133X
      6.2-9 [33X[0;0Y[10XBlockScalar[110X[133X
      6.2-10 [33X[0;0Y[10XLowerLeftPGroup[110X[133X
    6.3 [33X[0;0YMethods for projective groups[133X
      6.3-1 [33X[0;0Y[10XTrivialProjectiveGroup[110X[133X
      6.3-2 [33X[0;0Y[10XProjDeterminant[110X[133X
      6.3-3 [33X[0;0Y[10XReducibleIso[110X[133X
      6.3-4 [33X[0;0Y[10XBlocksModScalars[110X[133X
      6.3-5 [33X[0;0Y[10XNotAbsolutelyIrred[110X[133X
      6.3-6 [33X[0;0Y[10XSubfield[110X[133X
      6.3-7 [33X[0;0Y[10XDerived[110X[133X
      6.3-8 [33X[0;0Y[10XLowIndex[110X[133X
      6.3-9 [33X[0;0Y[10XC6[110X[133X
      6.3-10 [33X[0;0Y[10XTensor[110X[133X
      6.3-11 [33X[0;0Y[10XTwoLargeElOrders[110X[133X
      6.3-12 [33X[0;0Y[10XStabilizerChain[110X[133X
      6.3-13 [33X[0;0Y[10XBlockScalarProj[110X[133X
  7 [33X[0;0YExamples[133X
  
  
  [32X
