[GAP Forum] Product of Subgroups in a Group

[Sven Reichard]

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Am 15.02.2013 10:02, schrieb rahul kitture:
> Given two subgroups $H$ and $K$ of a finite group (say Symmetric/ 
> Alternating Group), how do we compute the product $HK$ in the
> group? I couldn't find anything from Help or topics in online
> library.

This may not be the most elegant way, but
gap> Group(Concatenation(List([H,K], GeneratorsOfGroup)), Identity(H));
should do the trick.

> Also, given finite number of square (invertible) matrices over a
> finite field, how do we get the (multiplicative) group, generated
> by them? (The command "GroupWithGenerators(); " does not work with
> the elements(generators) to be matrices.
> 
Works for me.

gap> GL(3, GF(2));
SL(3,2)
gap> List([1..3], x -> Random(last));
[ <an immutable 3x3 matrix over GF2>, <an immutable 3x3 matrix over GF2>,
  <an immutable 3x3 matrix over GF2> ]
gap> Group(last);
<matrix group with 3 generators>
gap> GroupWithGenerators(last2);
<matrix group with 3 generators>
gap> last=last2;
true

Are the entries of your matrices elements of the finite field? If not,
multiply the matrices by One(field).

HTH
Sven Reichard

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