[GAP Forum] Product of Subgroups in a Group

[Sandeep Murthy]

Hi,

If H, K are subgroups of G then

ListX( H, K, PROD )

will return a (mutable) list of
the elements of the set HK in
G.

Sincerely, Sandeep.

Sven Reichard wrote:
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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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