problem on group theory
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
80849
There does not exist group $G$ such that Aut$(G)\cong \mathbb{Z}_n$ (for odd $n$)
31252
"Efficient version" of Cayley's Theorem in Group Theory
151559
Please help: How to show that Aut(G) is a subgroup of Sym(G)
57309
Show that the free group on $n$ generators is a finite index subgroup of $F_2$
48692
A problem about the graph theory
71420
Prove that a group is abelian.
110708
On proving that a finitely generated group has a finite number of subgroups with index $n$.
149578
Subgroups of $(\mathbb Z_n,+)$
57809
For which $n$, $G$ is abelian?
42891
Prove that $Z(G)$ which is the center of $G$ is a subgroup of $G$
61226
Group Structure on $\Bbb R$
151621
$G$ a group and $H, K\mathrel{\unlhd}G$. Assuming that $H \cap K = \{1_G\}$ and $G = \langle H, K \rangle$, prove that $G \cong H \times K$
67554
In a group, the number of non-self-inverse elements is even
32735
If $ \langle G, \star \rangle $ is an abelian group, then for all $a, b \in G$, show that $(a \star b)^{n} = a^{n} \star b^{n}$.
130792
Commutator of a group
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian