Alexander Hulpke wrote:
Dear GAP Forum,
Jeffrey Rolland asked:
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 easiest seems to be to find all quotients of G1 that are isomorphic
to a subgroup of SL(2,5). (There is some redundancy in this and for
bigger cases other methods would be better. However in this case
everything else is far more work for the user.)
<snip>
Careful: This group has no quotient isomorphic to A_5 and thus cannot
have SL(2,5) as quotient. So its probably not the group you want.
<snip>
Best,
Alexander Hulpke
<snip>
Prof. Hulpke,
Oops! You are right. I actually want all homomorhphisms to Out(P) = Z_2.
I know you can just send z from the Z in G1 to 1 in Z_2 and the s and t
from the P in G1 to 0 in Z_2, but I needed to know if there were any
other homs. Sorry, it's been a long time since I looked at this, and I
forgot what I needed. I put this on the back burner until I realized GAP
may be able to do this.
At any rate, your post should give me what I need. Thanks.
Sincerely,
--
Jeffrey Rolland
<[EMAIL PROTECTED]>
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