If |Aut H| = 1 then how can I show H is Abelian? I've shown a mapping is an element of Aut H previously but didn't think that would help.(adsbygoogle = window.adsbygoogle || []).push({});

I have been looking through properties and theorems linked to Abelian groups but so far have had no luck finding anything that would help.

The closest I have is that it may have something to do with "any subgroup of an Abelian group is normal"

My line of argument was if |Aut G|=1 then Inn G = Aut G and so since Inn G is normal then G is normal?

However something tells me this is incorrect.

Thanks in advance for any help

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

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

# Order of Automorphism and Abelian Groups

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