PAUL HJELMSTAD wrote:
Can someone tell me what the right function is for the "Cartesian" style
group direct product?
(For example, D4 X S3)? I know they use the double-format for dihedral
groups, so this would
be Dihedral(8) I guess.
The one I have been playing with isn't right for my purposes, taking
sums instead of Cartesian products. I need the form that ends up with 12
terms in its cycle-structure G X H
Thanks
Paul,
the following may be what you were looking for:
DirectProductProductAction := function ( G, H )
local sum, domain, product;
sum := DirectProduct( G, H );
domain := Cartesian( [ 1 .. LargestMovedPoint( G ) ],
[ 1 .. LargestMovedPoint( H ) ] + LargestMovedPoint( G ) );
product := Action( sum, domain, OnTuples );
return product;
end
gap> D4 := Group((1,2,3,4),(1,3));
Group([ (1,2,3,4), (1,3) ])
gap> S3 := SymmetricGroup(3);
Sym( [ 1 .. 3 ] )
gap> DirectProductProductAction(D4, S3);
Group([ (1,4,7,10)(2,5,8,11)(3,6,9,12), (1,7)(2,8)(3,9),
(1,2,3)(4,5,6)(7,8,9)(10,11,12), (1,2)(4,5)(7,8)(10,11) ])
Sven.
--
Sven Reichard
School of Mathematics and Statistics
The University of Western Australia
35 Stirling Highway
Crawley 6009
Western Australia
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