# Simple, Abelian Groups

#### tiasum2

Need help with a proof:

Prove that a finite, simple, Abelian group must be isomorphic to Z_p for some prime p.

#### Drexel28

MHF Hall of Honor
Need help with a proof:

Prove that a finite, simple, Abelian group must be isomorphic to Z_p for some prime p.
Hint 1:

Since $$\displaystyle G$$ is abelian every subgroup is normal and so the only subgroups can be the trivial one or the full group.

Hint 2:

If $$\displaystyle G$$'s only subgroups are the trivial one or the full group it is cyclic/