Any group of order $p^2q^2$ is not simple for $p,q$ prime
51196
A group of order $p^2q^2$ is never simple
38853
Cyclic group of prime order
7973
Groups of order $pq$ have a proper normal subgroup
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
118022
Show that a group of order $180$ is not simple.
2731
Groups of even order have an element whose order is 2.
53207
Let $p$ be a prime. If a group has more than $p − 1$ elements of order $p$, why can’t the group be cyclic?
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
125640
Group of order $p^2$ is abelian.
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
622
Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$
104112
Number of finite simple groups of given order is at most $2$ - is a classification-free proof possible?
75127
Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$
42932
Prove that $p^j q^i$ cannot be a perfect number for $p, q$ odd, distinct primes.
53990
Group with more than one element and with no proper, nontrivial sub groups must have prime order.
116080
Let G be a finite group with more than one element. Show that G has an element of prime order