New posts in Sylow Theory

Show group of order $4563=3^3\cdot13^2$ is not simple.

Putnam 2007 A5: Finite group $n$ elements order $p$, prove either $n=0$ or $p$ divides $n+1$

A group of order 20

A finite group is nilpotent iff two elements with relatively prime order commute

Singular $p$-subgroups of a finite group

How many subgroups of order 17 does $S_{17}$ have?

$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$

Different Applications of Sylow Theorems

Normalizer of a Sylow 2-subgroups of dihedral groups

Every group of order $150$ has a normal subgroup of order $25$