If G is a nonabelian group with order of $p^3$ which p is a prime number then prove $G’=Z(G)$
106577
If G is not abelian with order $p^3$ then $G'=Z(G)$
22248
$G$ solvable $\implies$ composition factors of $G$ are of prime order.
47239
For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
13734
Show that every group of prime order is cyclic
66877
Showing groups of order $p^{k}(p+1)$ are not simple, p prime
8746
Groups of order $pq$ without using Sylow theorems
108830
Let $G$ be a group of order $2p$ , where $p$ is a prime greater than $2$. Then, G is isomorphic to $\mathbb{Z}_{2p}$ or $D_p$
141125
Group with order $p^2$ must be abelian . How to prove that?
17178
Order of $\phi(g)$ divides the order of $g$
63499
Groups of prime squared order
38153
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
156319
Show that a group with $|G| = 33$ contains an element of order $3$
19458
Finite groups and Normal subgroups - $G$ is a finite group such that $|G|=n$. Let $p$ be the smallest prime such that $p|n$.
75127
Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$
15630
Normal subgroup of prime order is characteristic
131488
Show that $p^3+4$ is prime
82037
Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$?