Prove that there does not exist group $G$ such that ${\rm Aut}(G)\cong \Bbb Z.$
72991
Is every group the automorphism group of a group?
157841
Existence of a non-abelian group of order $p^n$.
51145
Is it possible to prove $g^{|G|}=e$ in all finite groups without talking about cosets?
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
91021
Torsion elements of a group aren't necessarily a subgroup
35401
Examples of finite groups that are not a semidirect product
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
102912
Subgroups of finitely generated groups are not necessarily finitely generated
109060
Group containing no subgroup of index 2
86542
Group of positive rationals under multiplication not isomorphic to group of rationals
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
89508
Existence of normal subgroups for a group of order $36$
30753
Showing there is no ring whose additive group is isomorphic to $\mathbb{Q}/\mathbb{Z}$
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
55393
Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$