Let $G$ be a group. Prove that IF $x^2 = e$ for all $x \in G$, then $G$ is abelian.
20679
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
68971
Elementary approach to proving that a group of order 9 is Abelian
100605
let $G$ to be finite abelian group of order O(G), let n to be prime number and (O(G),n)=1 prove that $g=x^n$ for any $ x \in 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.
141125
Group with order $p^2$ must be abelian . How to prove that?
125640
Group of order $p^2$ is abelian.
36887
Suppose $G$ is a group of order 4. Show either $G$ is cyclic or $x^2=e$.
90332
Prove that that $U(n)$ is an abelian group.
5297
If G is a finite abelian group and $a_1,...,a_n$ are all its elements, show that $x=a_1a_2a_3...a_n$must satisfy $x^2=e$.
23394
If $G/Z(G)$ is cyclic, then $G$ is abelian
56650
Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions
46355
If $[G:H]=n$, is it true that $x^n\in H$ for all $x\in G$?
106577
If G is not abelian with order $p^3$ then $G'=Z(G)$
59128
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
102859
Proving that $G$ is a group if $a*x=b$ and $y*a=b$ have solutions.
74964
Showing Galois Group is Abelian