Definition:Sylow p-Subgroup

Let $$p$$ be prime. A Sylow $$p$$-subgroup of a finite group $$G$$ is a maximal $$p$$-subgroup $$P$$.

Maximality means that if $$Q$$ is a $$p$$-subgroup of $$G$$ and $$P \le Q$$, then $$P = Q$$.

Sylow $$p$$-subgroups are sometimes called $$p$$-Sylow subgroups.