How to prove that a group is abelian if $a^2=1$ for all $a \in A$.
101543
Let $A$ be a group, where $a^2=1$, a belongs to $A$. Prove that this group is commutative.
26148
A group such that $a^m b^m = b^m a^m$ and $a^n b^n = b^n a^n$ ($m$, $n$ coprime) is abelian?
152820
Every element of a group has order $2$. Why, intuitively, is it abelian?
17510
Proving a set is an abelian group.
60075
Does there exist an $n$ such that all groups of order $n$ are Abelian?
74586
Prove that every group of order $4$ is abelian
45760
if G is generated by {a,b} and ab=ba, then prove G is Abelian
134455
Any group of order $15$ is abelian(without sylow theorem)
23394
If $G/Z(G)$ is cyclic, then $G$ is abelian
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
23533
All subgroups normal $\implies$ abelian group
59128
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
57421
If $\forall x \in G$ where G is a group $x=x^{-1}$ then how is this group abelian?
76317
Let $C$ be the commutator subgroup of $G$. Prove that $G/C$ is abelian
57809
For which $n$, $G$ is abelian?