Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order

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This article describes a property that arises as the conjunction of a subgroup property: isomorph-normal 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 H of a group of prime power order P is termed an isomorph-normal coprime automorphism-invariant subgroup of group of prime power order if it satisfies both the following conditions:

  1. H is an isomorph-normal subgroup of P (in particular, it is an isomorph-normal subgroup of group of prime power order): In other words, for any subgroup K of P isomorphic to H, K is a normal subgroup of P.
  2. H is a coprime automorphism-invariant subgroup of P (in particular, it is a coprime automorphism-invariant subgroup of group of prime power order).


Relation with other properties

Stronger properties

Weaker properties