Automorphism

**hercules** · March 19th 2008, 06:46 AM

I need help with the following proof:
Prove that Aut( $\mathbb{Z}_{4}) \approx \mathbb{Z}_{2}$

Thanks

**ThePerfectHacker** · March 19th 2008, 07:03 AM

Note, $\mathbb{Z}_4 = \{ [0],[1],[2],[3] \} = \left< [1]\right>$ . Any homomorphism $\phi: \mathbb{Z}_4 \mapsto \mathbb{Z}_4$ is completely determined by $[1]$ (since it is the generator). Thus, there are four possibilities, $\phi([1]) = [0],\phi([1]) = [1], \phi([1]) = [2],\phi([1])= [3]$ . Which of these give rise to automorphisms?

Thread: Automorphism

LinkBack

Thread Tools

Display

Automorphism

Similar Math Help Forum Discussions

Automorphism

Automorphism

Automorphism

AutoMorphism

automorphism

Search Tags