If $G$ is a finite group such that $G / Z(G)$ is cyclic then $G$ is abelian
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Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
55976
Are groups satisfying $g=g^{-1}$ for all $g \in G$ abelian?
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Is every quotient of a finite abelian group $G$ isomorphic to some subgroup of $G$?
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A question on the group algebra $k[G]$ of a finite abelian group
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Prove or disprove: If $H$ and $G/H$ are cyclic, then $G$ is cyclic.
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A subgroup of a cyclic group is cyclic - Understanding Proof
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Product of two cyclic groups is cyclic iff their orders are co-prime
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Determine group G as cyclic
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Cyclic group $G$ with generator $ab$.
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If $G$ is a finite group and $|G| < |A| + |B|$, then $G=AB$.
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An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
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proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
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Prove or disprove: The automorphism group of a finite cyclic group must be cyclic.
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If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
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Extensions of finite cyclic groups
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How to show a group is cyclic?
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$