Coprime automorphism-invariant normal subgroup of group of prime power order
From Groupprops
This article describes a property that arises as the conjunction of a subgroup property: coprime automorphism-invariant normal subgroup with a group property imposed on the ambient group: group of prime power order
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup
Contents
Definition
A subgroup of a group of prime power order
is termed a coprime automorphism-invariant normal subgroup if it satisfies both these conditions:
- It is a normal subgroup of
: in particular, it is a normal subgroup of group of prime power order.
- It is a coprime automorphism-invariant subgroup of
: in particular, it is a coprime automorphism-invariant subgroup of group of prime power order.
Relation with other properties
Stronger properties
- Fusion system-relatively weakly closed subgroup
- Sylow-relatively weakly closed subgroup
- Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order