Can anybody help me out?(adsbygoogle = window.adsbygoogle || []).push({});

"Let G be a cyclic group of order 7. Determine the number of homomorphisms from G to [itex]S_7[/itex]"

I know the definition of a cyclic group. It's a group generated by a single element. The order 7 means that [itex] g^7 = e [/itex] for g within G.

I understand that a homomorphism is defined by [itex] \Psi (ab) = \Psi(a)\Psi(b)[/itex] for a, b that exist in G. [itex] \Psi : G \rightarrow S_7 [/itex]

My main problem is, I can't put this all together and answer the question!

Any comments/suggestions would be appreciated

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Homomorphism Q

**Physics Forums | Science Articles, Homework Help, Discussion**