Is Aut(A) Isomorphic to Aut(B) for Cyclic Groups of Different Orders?

[chibulls59]

Homework Statement

If A=<x> is a cyclic group of order 9 and B=<y> is a cyclic group of order 7. Deduce that Aut(A) is isomorphic to Aut(B)

Homework Equations

The Attempt at a Solution

I already proved that Aut(A) and Aut(B) are cyclic but I don't understand how they can be isomorphic if they don't have the same order. Also the groups are don't have the same amount of generators since both groups are cyclic so every element of both Aut(A) and Aut(B) are generators.

 

[Hurkyl]

I already proved that Aut(A) and Aut(B) are cyclic but I don't understand how they can be isomorphic if they don't have the same order.

They can't be. So you've either shown the problem is in error, of you've computed Aut(A) and Aut(B) incorrectly.

 

[chibulls59]

Oh I got it, for some reason I thought 9 was a prime number.