Proof of G being a cyclic group?
2104
Finite group for which $|\{x:x^m=e\}|\leq m$ for all $m$ is cyclic.
59128
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
104460
When a group is cyclic
39938
Subgroups of a cyclic group and their order.
98145
If $G$ is cyclic then $G/H$ is cyclic?
58014
Prove or disprove: The automorphism group of a finite cyclic group must be cyclic.
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
151025
If G is a group of order n=35, then it is cyclic
69046
Proof of $\mathbb{Q}$ is not cyclic
11003
Proving that $G/N$ is an abelian group
40993
Let $f:G\to G'$ be a surjective homomorphism. Prove that if $G$ is cyclic, then $G'$ is cyclic.
118898
Is there a simple way of proving that $\text{GL}_n(R) \not\cong \text{GL}_m(R)$?
61513
Prove that all cyclic groups of the same order are isomorphic
7967
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
24181
Showing that $G$ is a group under an alternative operation.
121810
Prove that the product of two infinite cyclic groups is not infinite cyclic.
154959
Proof of associativity of GCD?