[GAP Forum] Cartesian Group Direct Product

[PAUL HJELMSTAD]

Thanks, I know about that one. And you need to make them both Permutation 
Groups,
BTW, but what I really need is a Cartesian style (cross) product, as  a 
Group Direct Product,
I tried Semidirect Product but that doesn't seem to be it either.

Perhaps, it would be a simple program I could write to achieve the same 
result...


>From: "Justin C. Walker" <justin at mac.com>
>To: forum at gap-system.org
>Subject: Re: [GAP Forum] Cartesian Group Direct Product
>Date: Mon, 3 Dec 2007 22:13:51 -0800
>
>Dear Paul & Forum,
>
>On Dec 3, 2007, at 20:36 , 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
>
>The manual describes something called, suspiciously,  DirectProduct :-}.  
>Does that help?
>
>Trying your example:
>
>gap> D4:=DihedralGroup(4);
><pc group of size 4 with 2 generators>
>gap> S3:=SymmetricGroup(3);
>Sym( [ 1 .. 3 ] )
>gap> G:=DirectProduct(D4,S3);
><group of size 24 with 4 generators>
>
>and looking at G, it may not be quite what you want :-} (it's  combining a 
>PC group and a permutation group), but you may be able to  coax it into 
>something useful for you.
>
>FWIW, Gap comes with an index that covers all 5 of the manuals.
>
>Justin
>
>--
>Justin C. Walker, Curmudgeon at Large
>Director
>Institute for the Enhancement of the Director's Income
>-----------
>Nobody knows the trouble I've been
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>
>
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