[sglppow] 1 Introduction

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# 1 Introduction

SglPPow is a package which extends the Small Groups Library. Currently the Small Groups Library gives access to the following groups:

(1)
  Those of order at most 2000 except 1024 (423,164,062 groups);

(2)
  Those of cubefree order at most 50,000 (395,703 groups);

(3)
  Those of order p7 for the primes p=3,5,7,11 (907,489 groups);

(4)
  Those of order pn for n≤6 and all primes p;

(5)
  Those of order pqn where qn divides 28, 36, 55 or 74 and p is an arbitrary prime not equal to q;

(6)
  Those of squarefree order;

(7)
  Those whose order factorizes into at most 3 primes.

This package gives access to the groups of order p7 for p>11, and to the groups of order 38. The groups of order 38 have been determined by Michael Vaughan-Lee. The groups of order p7 for p>11 are available via Bettina Eick and Michael Vaughan-Lee's database of the nilpotent Lie rings of order pk for k≤7 and p>3. These groups are obtained from the Lie rings using the implementation of the Baker-Campbell-Hausdorff formula in the LieRing package. To access the groups of order p7 for p>11 you additionlly need Bettina Eick and Michael Vaughan-Lee's package LiePRing, and Willem de Graaf and Serena Cicalos's package LieRing.

Acknowlegdements: The authors thank Max Horn for help with general framework of GAP programms to extend the Small Groups Library.

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