If $(ab)^{3}=a^{3}b^{3}$ and $(ab)^{5}=a^{5}b^{5}$ for all $a,b \in G$ then $G$ is 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.
33593
An example of a non-abelian group $G$ where, for all $a,b\in G$, the equality $(ab)^{n}=a^{n}b^{n}$ holds for two consecutive integers $n$
106577
If G is not abelian with order $p^3$ then $G'=Z(G)$
112345
In an Integral Domain is it true that $\gcd(ac,ab) = a\gcd(c,b)$?
60075
Does there exist an $n$ such that all groups of order $n$ are Abelian?
138406
If N and every subgroup of N is normal in G then G/N is abelian .
13631
Showing group with $p^2$ elements is Abelian
33233
Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.
43783
Abelian group (Commutative group)
133627
If $\phi(g)=g^3$ is a homomorphism and $3 \nmid |G|$, $G$ is abelian.
23394
If $G/Z(G)$ is cyclic, then $G$ is abelian
7015
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
142375
Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
97565
Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$