- #1

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## Homework Statement

I am interested in proving that A

_{5}has no normal subgroups except itself and {e}.

## The Attempt at a Solution

Some proofs that I have seen use centralizers to do this, but since I haven't gone through that yet I think there should be some say to do it without them.

My approach would be to find the conjugacy classes of A

_{5}and use their orders to show that there cannot be a normal subgroup in A

_{5}since a normal subgroup is a union of conjugate classes.

But my main problem is how I should go about finding the conjugacy classes.

Thanks for your help.