New posts in Sylow Theory

Let G be a nonabelian group of order $p^3$, where $p$ is a prime number. Prove that the center of $G$ is of order $p$.

How many elements of order $7$ are there in a group of order $28$ without Sylow's theorem?

About the proof that a simple group of order 60 is isomorphic to A5

A group of order $30$ has a normal $5$-Sylow subgroup.

The intersection of a normal subgroup and Sylow $p$-subgroup

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