Here's one simpler solution, doing essentially the same thing you do, but
using a little more GAP machinery to do it more concisely:
gap> g := AlternatingGroup(5);
Alt( [ 1 .. 5 ] )
gap> h2 := Group((1,2)(3,4));
Group([ (1,2)(3,4) ])
gap> h3 := Group((1,2,3));
Group([ (1,2,3) ])
gap> h5 := Group((1,2,3,4,5));
Group([ (1,2,3,4,5) ])
gap> Action(g,Concatenation(RightCosets(g,h2),RightCosets(g,h3),
> RightCosets(g,h5)),OnRight);
<permutation group with 2 generators>
gap> NrMovedPoints(last);
62
Steve
On Wed, 9 Aug 2006 22:34:25 +0200
"Rudolf Zlabinger" <[EMAIL PROTECTED]> wrote:
> Dear Forums,
>
> i dealt with group A5 and the icosahedron. I was eager to know, how to let
> act A5 on the 62 endpoints of the 31 axes of the geometric model of the
> icosahedron group. As it was to expensive to simply use IsomorphicSubgroups
> to Symmetric Group 62 I developed a way using the action homomorphisms on the
> 2, 3 and 5 cycles cosets, as outlined in the attachment.
>
> I would like to know, whether there is a simpler way to do it, as I did,
> shown by the attachment containing a GAP session, only using permutation
> groups. If there is an error in my procedure, please give also feedback.
>
> Best regards, Rudolf Zlabinger
--
Steve Linton School of Computer Science &
Centre for Interdisciplinary Research in Computational Algebra
University of St Andrews Tel +44 (1334) 463269
http://www.dcs.st-and.ac.uk/~sal Fax +44 (1334) 463278
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