Sylow subgroup of normal subgroup
From Groupprops
This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: Sylow subgroup and normal subgroup
View other such compositions|View all subgroup properties
Contents
Definition
Symbol-free definition
A subgroup of a finite group is termed a Sylow subgroup of normal subgroup if it satisfies the following equivalent conditions:
- It is a Sylow subgroup of a normal subgroup of the whole group.
- It is the intersection of a normal subgroup of the whole group with a Sylow subgroup of the whole group.
- It is a Sylow subgroup inside its normal closure.
Equivalence of definitions
Further information: Equivalence of definitions of Sylow subgroup of normal subgroup