----- Original Message -----
From: "Steve Linton" <[EMAIL PROTECTED]>
To: "Rudolf Zlabinger" <[EMAIL PROTECTED]>
Cc: "Group Forum" <[EMAIL PROTECTED]>; "GAP Forum"
<[EMAIL PROTECTED]>
Sent: Thursday, August 10, 2006 11:58 AM
Subject: Re: [Group-pub-forum] A5 acting on 62 points
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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