Let $p<q$ be distinct prime numbers and $G$ be a group with $|G|=pq$
86025
Nonabelian semidirect products of order $pq$?
102971
Product of all elements of a finite group with an unique element of order 2
57427
Group of order $8p$ is solvable, for any prime $p$
77221
Prove that $G$ has a subgroup isomorphic to $G/H$.
22248
$G$ solvable $\implies$ composition factors of $G$ are of prime order.
67973
Prove that a finite abelian group is simple if and only if its order is prime.
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
62017
Distinct Sylow P subgroups
12862
Prove that two distinct numbers of the form $a^{2^{n}} + 1$ and $a^{2^{m}} + 1$ are relatively prime if $a$ is even and have $\gcd=2$ if $a$ is odd
19668
Does every group whose order is a power of a prime p contain an element of order p?
23885
Structure of a group, $G$, of order $pq$ where $p, q$ are prime.
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
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 $D_p$
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$
4402
Group of order $pqr$, $p < q < r$ primes
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.