p-subgroup ($P\le G,|P|=p^a$)

A p-subgroup is a subgroup which is a finite p-group, for a specified prime $p$. Every p-subgroup lies in a Sylow subgroup.

A p-subgroup is p-radical if it equals the p-core of its normalizer. Every defect group of a block is p-radical by defect groups are centralizer-conjugate Sylow intersections. Being an intersection of arbitrary Sylow subgroups alone is weaker than the centralizer-conjugate statement used in that argument.