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 (email@example.com).
All of the functions require a finite permutation group G and a prime p
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
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.