Finite-pi-potentially characteristic subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

Let K be a finite group and H be a subgroup of K. We say that H is finite-pi-potentially characteristic in K if there exists a finite group G containing K, such that every prime factor of G divides K, and H is a characteristic subgroup of G.

When K is a group of prime power order, this is termed finite-p-potentially characteristic subgroup.

Relation with other properties

Stronger properties

Weaker properties