1) State Sylow's theorem for abelian groups.

2) Let G be a group, write the class equation for G.

3) Find each of the term in the class equation in 2) for the group S3, and write the expression of the class equation for S3?

4) If p is a prime number, then any group G of order p^2 is abelian?

Problem 8. (18 points) (1) State Sylow's theorem for abelian groups. (2) Let G be a group. Write the class equation for G. (3) Find each of the term in the class equation in (2) for the group 33 and write the expression of the class equation for 8'3. (4) Prove that if p is a prime number then any group G of order p2 is abelian