Coprime automorphism-invariant 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 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
Definition
A subgroup of a group of prime power order (i.e., a finite
-group for some prime number
)
is termed a coprime automorphism-invariant subgroup if it is invariant under all the
-automorphisms, i.e., the automorphisms whose order is relatively prime to
.
Relation with other properties
Stronger properties
- Characteristic subgroup of group of prime power order
- Coprime automorphism-invariant normal subgroup of group of prime power order
- Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order
- Sylow-relatively weakly closed subgroup
- Fusion system-relatively weakly closed subgroup