Show that the group $G$ is abelian if $G/Z(G)$ is cyclic
102146
If a group mod its commutator subgroup is cyclic, then the group is abelian?
4838
For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian
68971
Elementary approach to proving that a group of order 9 is Abelian
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
31380
Exponent and abelian groups
135188
Show that if $\vert G\vert = pq$, then either $G$ is abelian or $Z(G) = \{ e\}$.
59007
Suppose $|G| = 105$. Show that it is abelian if it has a normal $3$-Sylow subgroup.
65900
Show that a finite group with certain automorphism is abelian
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
17510
Proving a set is an abelian group.
98145
If $G$ is cyclic then $G/H$ is cyclic?
5223
$\mathbb{Z}_m \times \mathbb Z_n$ is cyclic if and only if $\gcd(m,n)=1$
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
101596
Determine group G as cyclic
68733
If $G/Z(G)$ is cyclic then $G$ is abelian – what is the point?
142375
Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.
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.