Show that there exists a group of order $p^{3}$, with p prime.
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
7973
Groups of order $pq$ have a proper normal subgroup
122970
A question on $p$-groups, and order of its commutator subgroup.
157841
Existence of a non-abelian group of order $p^n$.
76446
Why are cyclic groups of order $p$ (prime) unique up to isomorphism?
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
70066
Show that product of primes, $\prod_{k=1}^{\pi(n)} p_k < 4^n$
28266
For $n\geq 3$ there exist $x,y\in S_n$ such that $x$ and $y$ have order $2$ and $xy$ has order $n$.
103423
Normal subgroup where G has order prime
100605
let $G$ to be finite abelian group of order O(G), let n to be prime number and (O(G),n)=1 prove that $g=x^n$ for any $ x \in G$
21673
If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
22248
$G$ solvable $\implies$ composition factors of $G$ are of prime order.
125640
Group of order $p^2$ is abelian.
19016
Given 3 distinct primes {$p,q,r$}, then $|G|=pqr \implies G$ not simple
4402
Group of order $pqr$, $p < q < r$ primes
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$