Finite-pi-potentially characteristic subgroup

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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