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%W intro.tex GAP documentation Bettina Eick
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\Chapter{Introduction}
SglPPow is a package which extends the Small Groups Library. Currently the
Small Groups Library gives access to the following groups:
\beginitems
<(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 $p^{7}$ for the primes $p=3,5,7,11$ (907,489 groups);
<(4)> & Those of order $p^{n}$ for $n\leq 6$ and all primes $p$;
<(5)> & Those of order $pq^{n}$ where $q^{n}$ 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.
\enditems
This package gives access to the groups of order $p^{7}$ for primes
$p>11$, and to the groups of order $3^{8}$.
To access the groups of order $p^{7}$ for primes $p>11$ you need the
packages LiePRing (by Michael Vaughan-Lee and Bettina Eick) and LieRing
(by Willem de Graaf and Serena Cicalo).
The groups of order $3^{8}$ have been determined by Michael Vaughan-Lee.
The groups of order $p^{7}$ for primes $p>11$ are available via the
database of the nilpotent Lie rings of order $p^{k}$ for $k\leq 7$ and
primes $p>3$ in the LiePRing package. These groups are obtained from the
Lie rings using the implementation of the Baker-Campbell-Hausdorff formula
in the LieRing package.
{\bf Acknowledgements:} The authors thank Max Horn for help with general
framework of GAP programs to extend the Small Groups Library.
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