# Abstract algebra- isomorphisms

1. Feb 26, 2014

### tom2014

1. The problem statement, all variables and given/known data
Let $A=C_{p^k}$ where $p$ is a prime and $k>0$. Let $_{p^m} A$consist of all element a of A such that $a^{p^m}=e$.

Prove that $_{p^m} A/_{p^m-1} A\cong C_p$ if $m\leq k$, $\frac{_{p^m} A}{_{p^m-1} A}=e$ if $m>k$

3. The attempt at a solution

Please could someone explain how to get started with this proof, I have no idea.

2. Feb 26, 2014

### kduna

Have you heard of the first Isomorphism Theorem? That should do the trick.