Sylow subgroup of normal subgroup

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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

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:

  1. It is a Sylow subgroup of a normal subgroup of the whole group.
  2. It is the intersection of a normal subgroup of the whole group with a Sylow subgroup of the whole group.
  3. It is a Sylow subgroup inside its normal closure.

Equivalence of definitions

Further information: Equivalence of definitions of Sylow subgroup of normal subgroup

Relation with other properties

Stronger properties

Weaker properties