Finite p-groups [HB 24]

A new version of the p-quotient algorithm has been installed, and various bugs related to the p-quotient process have been fixed.

The code to construct the standard presentation of a p-group, the automorphism group of a p-group, and to generate descriptions of p-groups has been completely replaced. Much of the existing C code for these computations has been withdrawn and replaced by a package of Magma language functions. The interfaces for these functions have been significantly modified and (hopefully) simplified. Many of the problems in the use of these functions which were related to external file handling should now disappear.

Changes:

• The arguments for GeneratepGroups have changed. Many of the optional arguments are no longer supported. The function Descendants has been introduced which constructs the descendants [certain central extensions] of a p-group.

• The input argument for the function StandardPresentation is now restricted to GrpPC; inputs of type GrpFP are no longer supported.

New Features:

• The function StartNewClass has been introduced which is used to inform the pQuotientProcess that the user is about to start a new class computation.
• The function pCoveringGroup has been introduced which constructs the p-covering group for a p-group.

• The range of application of AutomorphismGroup has been significantly extended.
• The function ClassTwo has been introduced which counts precisely the number of p-class 2 p-groups of various orders.

• The function UnipotentStabiliser, given as input a unipotent subgroup G of GL (d, F) and U a subspace of the natural vector space, determines the stabiliser in G of U.

• The function OrderAutomorphismGroupAbelianPGroup computes the order of the automorphism group of an abelian p-group.
• The function NumberOfSubgroupsAbelianPGroup has been introduced which computes the number of subgroups of an abelian p-group.