Group G with $\left(\forall g \in G: g^2=1_G\right) \implies \text{G is abelian}$
20679
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
112407
Set of left cosets is a group
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
76317
Let $C$ be the commutator subgroup of $G$. Prove that $G/C$ is abelian
24181
Showing that $G$ is a group under an alternative operation.
158074
Cyclic group $G$ with generator $ab$.
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
150585
Group with $a=a^{-1}$ for all $a\in G$ is abelian
66510
A group is abelian if and only if the center of the group is all the group
105180
When does $(ab)^n = a^n b^n$ imply a group is abelian?
106123
Is there a finite abelian group $G$ such that $\textrm{Aut}(G)$ is abelian but $G$ is not cyclic?
158490
Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
106809
$f: G→G$ defined by $f(x) =x^2$ is a homomorphism if and only if $G$ is abelian.
152820
Every element of a group has order $2$. Why, intuitively, is it abelian?
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.
89234
Any Set with Associativity, Left Identity, Left Inverse is a Group
4838
For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian