How to prove that if group $G$ is abelian, $H = \{x \in G : x = x^{-1}\}$ is a subgroup?
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
4838
For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
153797
Is a quotient group a subgroup?
34724
For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable?
71420
Prove that a group is abelian.
43783
Abelian group (Commutative group)
46355
If $[G:H]=n$, is it true that $x^n\in H$ for all $x\in G$?
52105
Prove that $HK$ is a subgroup iff $HK=KH$.
55350
H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.
56650
Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions
140334
Let $G$ be a group and $H$ be a subgroup of $G$ of index $2$ .Then show that if $a,b\notin H$ then $ab\in H$.
97565
Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
68971
Elementary approach to proving that a group of order 9 is Abelian
65744
How can I Prove that H=G or K=G
60208
Proof of property of abelian group