Finite group for which $|\{x:x^m=e\}|\leq m$ for all $m$ is cyclic.
35664
If $x^m=e$ has at most $m$ solutions for any $m\in \mathbb{N}$, then $G$ is cyclic
38853
Cyclic group of prime order
101596
Determine group G as cyclic
84823
When is the group of units in $\mathbb{Z}_n$ cyclic?
28362
Product of two cyclic groups is cyclic iff their orders are co-prime
147517
Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
147596
Number of solutions to $x^n=e$ in group $G$ is divisible by $n$
90437
Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.
102146
If a group mod its commutator subgroup is cyclic, then the group is abelian?
104460
When a group is cyclic
152662
Proving that any finite cyclic group of order $n$ is isomorphic to $$
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?
114590
Prove that any finite group $G$ of even order contains an element of order $2.$
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
23394
If $G/Z(G)$ is cyclic, then $G$ is abelian
5223
$\mathbb{Z}_m \times \mathbb Z_n$ is cyclic if and only if $\gcd(m,n)=1$
40993
Let $f:G\to G'$ be a surjective homomorphism. Prove that if $G$ is cyclic, then $G'$ is cyclic.