If G is a group such that $(a.b)^{2}=a^{2}.b^{2}$ for all a and b,Then show that G is abelian
43783
Abelian group (Commutative group)
60208
Proof of property of abelian group
152630
showing that a group of order 45 is abelian
150585
Group with $a=a^{-1}$ for all $a\in G$ is abelian
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
134403
Let $G$ be a group, and let $n\in\mathbb Z$. Show that $(ab)^n=a^nb^n\iff(ab)^{1-n}=a^{1-n}b^{1-n}$.
106809
$f: G→G$ defined by $f(x) =x^2$ is a homomorphism if and only if $G$ is abelian.
52357
If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.
6153
Suppose that $G$ is a group with the property that for every choice of elements in $G$, $axb=cxd$ implies $ab=cd$. Prove that $G$ is Abelian.
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
98542
Prove that $H$ is a subgroup of an abelian group $G$
66510
A group is abelian if and only if the center of the group is all the group
59128
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
152820
Every element of a group has order $2$. Why, intuitively, is it abelian?
74586
Prove that every group of order $4$ is abelian
41977
If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$
101543
Let $A$ be a group, where $a^2=1$, a belongs to $A$. Prove that this group is commutative.