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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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