[GAP Forum] Fw: A5 acting on 62 points

[Rudolf Zlabinger]

----- Original Message ----- 
From: "Steve Linton" <sal at dcs.st-and.ac.uk>
To: "Rudolf Zlabinger" <Rudolf.Zlabinger at chello.at>
Cc: "Group Forum" <group-pub-forum at lists.maths.bath.ac.uk>; "GAP Forum"
<forum at gap-system.org>
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" <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
>


_______________________________________________
Forum mailing list
Forum at mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum