let $G$ is finite group and has a unique maximal subgroup $H$, show that it is cyclic.
12912
Finite groups with exactly one maximal subgroup
65968
Prove that any two cyclic groups of the same order are isomorphic?
2104
Finite group for which $|\{x:x^m=e\}|\leq m$ for all $m$ is cyclic.
124455
Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$
133298
Assume $|G|=40$. Show that the subgroup of order $8$ is normal and unique.
61394
The product of finitely many cyclic groups is cyclic
58397
Every cyclic group with order > 2 has at least 2 distinct generators
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
124150
Faithful representation implies group is cyclic
151619
A finite abelian group containing a non-trivial subgroup which lies in every non-trivial subgroup is cyclic
98145
If $G$ is cyclic then $G/H$ is cyclic?
11825
Let $H$ be a subgroup of $G$. Let $K = \{x \in G: xax^{-1} \in H \iff a \in H\}$. Prove that $K$ is a subgroup of $G$.
14890
Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?
36040
A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
121587
Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$