(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am interested in proving that A_{5}has no normal subgroups except itself and {e}.

3. 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Conjugacy Groups of A5

**Physics Forums | Science Articles, Homework Help, Discussion**