Showing Aut of G is a group
43759
Prove that the set $\mathrm{Aut}(G)$ of all automorphisms of the group $G$ with the operation of taking the composition is a group
17510
Proving a set is an abelian group.
130706
Group presentations and the Dihedral Group
70394
Prove that $a * b$ is a group (Hungerford, 2nd ed., sec $7.2$, Exercise $22$)
7890
Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
33196
show that A(T) is a group under operation of composition of functions
76863
How to show $ \sup \inf g(x,y) \leq \inf \sup g(x,y)$?
37971
Prove that the center of a group is a normal subgroup
112407
Set of left cosets is a group
148881
Aut(GxH) isomorphic to Aut(G)xAut(H)
52121
Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.
144258
How to show a group is cyclic?
98507
$\text{Aut}(F)$ is isomorphic to the multiplicative group of all $n\times n$ matrices over $\mathbb Z$
107716
Show that $G$ is cyclic
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
26449
$|G|=24$ prove that $G$ is not simple
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian