- #1

- 308

- 0

## Homework Statement

Prove that [tex]Aut(Z_2\oplus Z_4) \cong D_8[/tex]

## Homework Equations

## The Attempt at a Solution

To start,

I wrote out all of the elements of [tex]Z_2\oplus Z_4[/tex]. There are 8 of them, of course. Then I need to find the automorphisms of it. It looks to me like they would be the same as Aut(D8),which I have. I have proved (I think) that [tex]Aut(D_8)\cong D_8[/tex]. I'm just unsure HOW to go about this one.

Could I show with a cayley table that [tex]Z_2\oplus Z_4[/tex] is nonabelian and it's clearly of order 8, so then the isomorphism holds?

I just get stuck on these types of problems. the idea of isomorphisms is still pretty fresh to me and so are the groups themselves.

Any help will be appreciated.

Thanks

CC

Last edited: