The order of the ${\rm Aut}(G)$, where $G$ is a $p$-group is divisible by $p$.
123796
Order of automorphism group of a $p$-group is divisible by $p$.
110390
Order of group $GL_{2}\left( \mathbb{F}_{p}\right) $
119758
On the order of elements of $\mathrm{GL}(2,q)$.
121481
Non-abelian finite $p$-group in which every element has prime order?
157841
Existence of a non-abelian group of order $p^n$.
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
126893
A group of order 2p (p prime) and other conditions - prove abelian.
8746
Groups of order $pq$ without using Sylow theorems
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
88440
Is G a CLT group if its order is product of distinct prime?
17316
If $a^\phi = 1$ then the order of $a$ divides $\phi$
15387
Order of $GL(n, \mathbb Z_p)$
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
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
141125
Group with order $p^2$ must be abelian . How to prove that?
15526
Question on groups of order $pq$