This chapter describes the GAP accessible functions of the SISYPHOS (Version~0.6) share library package for computing with modular group algebras of p-groups, namely a function to convert a p-group into SISYPHOS readable format (see PrintSisyphosInputPGroup), several functions that compute automorphism groups of p-groups (see Automorphisms), functions that compute normalized automorphism groups as polycyclically presented groups (see AgNormalizedAutomorphisms, AgNormalizedOuterAutomorphisms), functions that test two p-groups for isomorphism (see IsIsomorphic) and compute isomorphisms between p-groups (see Isomorphisms), and a function to compute the element list of an automorphism group that is given by generators (see AutomorphismGroupElements).
The SISYPHOS functions for group rings are not yet available, with the only exception of a function that computed the group of normalized units (see NormalizedUnitsGroupRing).
The algorithms require presentations that are compatible with a
characteristic series of the group with elementary abelian factors, e.g.
the p-central series.
If necessary such a presentation is computed secretly using the
p-central series, the
computations are done using this presentation, and then the results are
carried back to the original presentation. The check of compatibility
is done by the function
isCompatiblePCentralSeries of the group will be either
If you know in advance that your group is compatible with a series of the
kind required, e.g. the Jennings-series,
you can avoid the check by setting this flag to
true by hand.
Before using any of the functions described in this chapter you must load the package by calling the statement
gap> RequirePackage( "sisyphos" );