1. ## Quotient group

Assume N is a normal subgroup of G.
a) Prove that if [G:N] is a prime, then G/N is cyclic. (could you provide an example as well)
b) Prove or disprove the converse of the statement in part (a).

Thank You.

2. Originally Posted by hercules

Assume N is a normal subgroup of G.
a) Prove that if [G:N] is a prime, then G/N is cyclic. (could you provide an example as well)
b) Prove or disprove the converse of the statement in part (a).
a)If $G$ is a finite group then $|G/N| = [G:N]$. Prime groups are cyclic, so $G/N$ is cyclic.
b)It is false. Try something.

3. Originally Posted by ThePerfectHacker
a)If $G$ is a finite group then $|G/N| = [G:N]$. Prime groups are cyclic, so $G/N$ is cyclic.
b)It is false. Try something.

wow....lightening quick response ...thank you.

4. Originally Posted by hercules
wow....lightening quick response ...thank you.
I am the fastest responder in the West.

Also, why would this Forum claim to be the fastest responding forum on the internet if it was not true?