- #1
mathusers
- 47
- 0
thnx for helping on the previous post.
heres the next one, as usual any hints on how to approach the question would be greatly appreciated. i will attempt the questions with the hints :)
(1)
describe explicitly all homomorphisms
\varphi : C_4 \rightarrow Aut(C_5)
(2)
For each such homomorphism \varphi describe the semidirect product C_5 \rtimes_{\varphi} C_4 in terms of generators and relations.
(3) How many distinct isomorphism types of groups of the form C_5 \rtimes_{\varphi} C_4 are there?
heres the next one, as usual any hints on how to approach the question would be greatly appreciated. i will attempt the questions with the hints :)
(1)
describe explicitly all homomorphisms
\varphi : C_4 \rightarrow Aut(C_5)
(2)
For each such homomorphism \varphi describe the semidirect product C_5 \rtimes_{\varphi} C_4 in terms of generators and relations.
(3) How many distinct isomorphism types of groups of the form C_5 \rtimes_{\varphi} C_4 are there?
