1
$\begingroup$

In group $S_5$ let's take the subgroup $H$ generated by permutations $a=(2\,3\,5)$ and $b=(3\,2\,5)$. Find AutH.

So, I have found out that $ab=ba=e$ and $aa=b$ and $bb=a$. So $H$ is $\{e,a,b\}$. Is $\operatorname{Aut}H$ isomorphic to $\Bbb Z_3$? Are there any others isomorphisms? Thanks.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.