Finite-pi-potentially fully invariant 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]


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

Relation with other properties

Stronger properties

Weaker properties