- #1

halvizo1031

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## Homework Statement

let p be a prime number and let G be a group with order p^2. the task is to show that G is either cyclic or isomorphic to Zp X Zp.

a. let a, not equal to the identity,be an element in G and A=<a>. What's the order of A.

b. consider the cosets of A: G/A={A,g2A,...gnA}. What's the value of n?

## Homework Equations

## The Attempt at a Solution

for part a, does the order of A have to do with the index of A in G? If so, how?

for part b, can i use the fact that the index of A divides the order of G? If so, how?