Let G be a group with $|G|=p^{2}$ , prove that G is cyclic.
125640
Group of order $p^2$ is abelian.
75127
Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$
152071
Group $G$ is cyclic $\iff$ every subgroup of $G$ has the form $G^k$, where $G^k=\{g^k\mid g\in G\}$
117899
At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic
58397
Every cyclic group with order > 2 has at least 2 distinct generators
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
156429
If $G$ is a group whereby $(a\cdot b)^{i} =a^i\cdot b^i$ for three consecutive integers $i$ for all $a, b \in G$, show $G$ is abelian.
13734
Show that every group of prime order is cyclic
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
155219
Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.
126893
A group of order 2p (p prime) and other conditions - prove abelian.
105671
Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$
118894
Cyclic subgroup of dihedral group
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?
117206
$|G|$ and $|{\rm Aut}(G)|$ are relatively prime $\Rightarrow$ $G$ should be cyclic?
114590
Prove that any finite group $G$ of even order contains an element of order $2.$
84501
Proof involving Cyclic group, generator and GCD