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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