[GAP Forum] Use GAP to Compute Hom(G1, G2)?
rollandj at uwm.edu
Fri Feb 8 21:57:44 GMT 2008
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.
<rollandj at uwm.edu>
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