I want to show that Aut$K_4\cong S_3$, where $K_4$ is the Klein's 4-group. I have shown that there exist 6 automorphsms from $K_4$ to $K_4$. But how to show that Aut$K_4$ is nonabelian?
Asked
Active
Viewed 156 times
0
-
2This is a duplicate of *. – Mikasa Dec 05 '13 at 16:19
1 Answers
1
There are group $3$ elements of order $2$ in $\bf{V}$ has so every $\phi\in\text{Aut}(\bf{V})$ permutes the $3$ involutions. By taking $G=\mathbf{V}-\{1\}$ which is of order $3$ then $$\phi\mapsto \phi|_{G}$$ is a homomorphism from $\text{Aut}(\bf{V})$ to $S_G$. Show that this map is an isomorphism.
Mikasa
- 67,374