2005-8.md

course	course_year	question_number	tags	title	year
Groups, Rings and Modules	IB	8	IB 2005 Groups, Rings and Modules	2.I.2C	2005

Define an automorphism of a group $G$, and the natural group law on the set $\operatorname{Aut}(G)$ of all automorphisms of $G$. For each fixed $h$ in $G$, put $\psi(h)(g)=h g h^{-1}$ for all $g$ in $G$. Prove that $\psi(h)$ is an automorphism of $G$, and that $\psi$ defines a homomorphism from $G$ into $\operatorname{Aut}(G)$.