- #1
RVP91
- 50
- 0
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.
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
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