New posts in Simple Groups

Let $n=p^mr$ where $p$ is prime and $r\in\mathbb{Z_{>1}}$ such that $p\nmid r$. If $G$ is a simple group of order $n$ then $p^m\mid(r-1)!$

Nonexistence of a simple group of order 576

Nonexistence of a simple group of order 420

A "functional" definition of simple group?

Show that the group is not simple

How are simple groups the building blocks?

Sort-of-simple non-Hopfian groups

Every normal subgroup of a finite group is contained in some composition series

$A_6 \simeq \mathrm{PSL}_2(\mathbb{F}_9) $ only simple group of order 360

Distinct Sylow $p$-subgroups intersect only at the identity, which somehow follows from Lagrange's Theorem. Why?