If a is self-inverse, then the group is abelian
1364
Let $G$ be a group in which $a^2=e$ for all elements of $a$ of $G$. Show that $G$ is Abelian.
145159
Finite group is abelian if the representatives of its conjugacy classes commute
57809
For which $n$, $G$ is abelian?
90332
Prove that that $U(n)$ is an abelian group.
98542
Prove that $H$ is a subgroup of an abelian group $G$
27905
Let $G$ be a group, where $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5$. Prove that $G $ is an abelian group.
126893
A group of order 2p (p prime) and other conditions - prove abelian.
23533
All subgroups normal $\implies$ abelian group
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
116737
An element of a group $G$ is not conjugate to its inverse if $\lvert G\rvert$ is odd
17510
Proving a set is an abelian group.
20679
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
59211
Product of Finite Abelian Group
80976
Direct Product Of Abelian Group
83938
If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
71035
Non abelian subgroup of a abelian group.
135039
${\rm Aut}(G)$ is cyclic $\implies G$ is abelian