> < ^ Date: Sun, 30 Jan 2000 15:44:51 +0100 (MET)
> < ^ From: Bettina Eick <beick@tu-bs.de >
< ^ Subject: Re: Question on 'Extensions'

Dear Michael Leithold,

I have gap 4.1 and I compute all extensions of G by a G-module M with
'Extensions'. Is there a function which returns the module M as a
subgroup of an extension F? Or at least returns M as a group?

I think there is currently only one method for `Extensions' in the
GAP 4 library and that is the method for a finite soluble group G.
For this case, I enclose below a function which returns the elementary
abelian normal subgroup of the extension F which corresponds to the
given module.

With the next GAP 4 release I will also add a similar method to the GAP

Best wishes,
         Bettina Eick

## F is the extension of the finite soluble group G with a G-module M
ModuleOfExtension := function( G, F )
    local n, m;
    n := Length(Pcgs(G));
    m := Length(Pcgs(F));
    return Subgroup(F, Pcgs(F){[n+1..m]} );

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