Groups - Prove that if $G/Z(G)$ is cyclic then $G$ is abelian
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
1364
Let $G$ be a group in which $a^2=e$ for all elements of $a$ of $G$. Show that $G$ is Abelian.
152071
Group $G$ is cyclic $\iff$ every subgroup of $G$ has the form $G^k$, where $G^k=\{g^k\mid g\in G\}$
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
102146
If a group mod its commutator subgroup is cyclic, then the group is abelian?
76317
Let $C$ be the commutator subgroup of $G$. Prove that $G/C$ is abelian
20679
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
83938
If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
71420
Prove that a group is abelian.
36887
Suppose $G$ is a group of order 4. Show either $G$ is cyclic or $x^2=e$.
116707
Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.
40287
Prove: if $a,b\in G$ commute with probability $>5/8$, then $G$ is abelian
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
106577
If G is not abelian with order $p^3$ then $G'=Z(G)$
74586
Prove that every group of order $4$ is abelian