> < ^ Date: Thu, 25 May 1995 11:42:00 +0100
> < ^ From: Derek Holt <dfh@maths.warwick.ac.uk >
> < ^ Subject: Re: Upgrade for GAP 3.4 patchlevel 1 (V3R4P1) to patchlectl 2 (V3R4P2)

Re: New Cohomology Package in GAP 3.4.

Here is a brief summary of what this package can do - see the manual
chapter for details on the GAP functions. Any problems or questions about
this package should probably be directed to me.
I uses a Bourne Shell script, and so will presumably only work on UNIX machines.

Derek Holt (dfh@maths.warwick.ac.uk).

All of the functions require a finite permutation group G and a prime p
as input.
Some of them require a finitely presented group F isomorphic to G,
in which the generators correspond to those of G.
Others require a finite dimensional KG-module M, where K is the finite field
of order p, and M is defined by a list of matrices over K corresponding to
the generators of G.

1. The p-component S_p of the Schur Multiplier (S = H_2(G) ) of G can be
computed (as a list of orders of the invariant factors).

2. Given F as above, a presentation of a covering group of S_p by G can
be computed.

3. Given M as above, the dimensions of the first and second cohomology groups
H^1(G,M) and H^2(G,M) over K can be computed.

4. Given F and M as above, presentations of the extensions (split and nonsplit)
of M by G can be computed.

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