Finite-pi-potentially verbal 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]


Suppose K is a finite group and H is a subgroup of K. We say that H is a finite-pi-potentially verbal subgroup of K if the following holds: There exists a group G containing K such that all prime factors of the order of G also divide the order of K and H is a verbal subgroup of G.

Relation with other properties

Stronger properties

Weaker properties