If $(ab)^3=a^3 b^3$, prove that the group $G$ is abelian.
92193
Problem from Herstein on group theory
111886
Let $(G,•)$ be a group in which $(a•b)^3 = a^3•b^3$. Prove that $H=\{x^3 : x \in G\}$ is a normal subgroup of $G$.
74964
Showing Galois Group is Abelian
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
59007
Suppose $|G| = 105$. Show that it is abelian if it has a normal $3$-Sylow subgroup.
89184
Prove $30|(a^3b-ab^3) $
13742
Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
79452
How to prove that it is a group?
135188
Show that if $\vert G\vert = pq$, then either $G$ is abelian or $Z(G) = \{ e\}$.
133627
If $\phi(g)=g^3$ is a homomorphism and $3 \nmid |G|$, $G$ is abelian.
152630
showing that a group of order 45 is abelian
49768
If Gal(K,Q) is abelian then |Gal(K,Q)|=n
117815
Non-abelian group $G$ satisfying $(a \cdot b)^i=a^i \cdot b^i,$ for two consecutive integers.
3838
If a group satisfies $x^3=1$ for all $x$, is it necessarily abelian?
83938
If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
150585
Group with $a=a^{-1}$ for all $a\in G$ is abelian