# Groups of order p^2 where p is prime

1. Dec 5, 2009

### halvizo1031

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

3. 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?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution