Let $G$ be a group, where $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5$. How to prove that $G$ is an abelian group?
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.
106577
If G is not abelian with order $p^3$ then $G'=Z(G)$
125559
In a group $G$, if for all $a,b,c\in G$, $ab=ca\Rightarrow b=c$, then $G$ is abelian
61732
Prove any group with 3 elements is isomorphic to $\mathbb{Z}_3$
143550
Order of product of two elements in an abelian group
25439
f(a) = inverse of a is an isomorphism iff a group G is Abelian
156429
If $G$ is a group whereby $(a\cdot b)^{i} =a^i\cdot b^i$ for three consecutive integers $i$ for all $a, b \in G$, show $G$ is abelian.
59007
Suppose $|G| = 105$. Show that it is abelian if it has a normal $3$-Sylow subgroup.
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
60208
Proof of property of 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 $x^2=e$.
139100
A question on the group algebra $k[G]$ of a finite abelian group
102742
order $a$ = 5, $a^3b = ba^3$. show that that $ab = ba$.
71232
if $A$ is Abelian group , $B$ is subgroup of $A$ , Is $B \times A/B \cong A$?
20679
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
125640
Group of order $p^2$ is abelian.
57421
If $\forall x \in G$ where G is a group $x=x^{-1}$ then how is this group abelian?