[GAP Forum] Use GAP to Compute Hom(G1, G2)?

Jeffrey Rolland rollandj at uwm.edu
Fri Feb 8 21:57:44 GMT 2008

Hello, all!

I am a newbie to GAP.

I am trying to compute the set of all homomorphisms from a group G1 
[which is the semi-direct product of the integeres Z with the binary 
icosahedral group P (also known as SL(2,5) and the Poincare group)] to 
the group P (the Poincare group again) - Hom(G1, P). This sort of 
problem seems right up GAP's alley.

I have a presentatiion for G1: <z, s, t| s^3(st)^(-2), t^5(st^(-2), 
zs(s^2ts^2t^3z)^(-1), zt(s^5ts^2tz)^(-1)>. (The first two relators 
recreate the Poincare group; the second two relators give the 
consequences for sliding the "z" past the "s" and the "t", 
respectively.) The group G1 satisfies the short exact sequence 1 -> P -> 
G1 -> Z - 1; it is the only group (other than ZxP) to do so (up to 

If anyone can help me compute this set of homomorphisms from G1 to P, I 
would greatly appreciate it.

Jeffrey Rolland
<rollandj at uwm.edu>

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