Proving group is cyclic without Fundamental Theorem of finite Abelian groups?
31511
A finite abelian group that does not contain a subgroup isomorphic to $\mathbb Z_p\oplus\mathbb Z_p$, for any prime $p$, is cyclic.
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
68733
If $G/Z(G)$ is cyclic then $G$ is abelian – what is the point?
58014
Prove or disprove: The automorphism group of a finite cyclic group must be cyclic.
112933
Show that $Z\times Z$ is not cyclic...
65968
Prove that any two cyclic groups of the same order are isomorphic?
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
13631
Showing group with $p^2$ elements is Abelian
61394
The product of finitely many cyclic groups is cyclic
155219
Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.
76504
Non-trivial cyclic group with unique generator
124455
Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$
25235
Finite abelian groups - direct sum of cyclic subgroup
73402
Showing that $(\mathbb{Z}/p^{a}\mathbb{Z})^*$ is a cyclic group
17510
Proving a set is an abelian group.
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
17077
Prove or disprove: If $H$ and $G/H$ are cyclic, then $G$ is cyclic.