[GAP Forum] Re: [Group-pub-forum] A5 acting on 62 points

[Steve Linton]

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" <Rudolf.Zlabinger at chello.at> 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