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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.

