Finite-pi-potentially verbal subgroup
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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 is a finite group and is a subgroup of . We say that is a finite-pi-potentially verbal subgroup of if the following holds: There exists a group containing such that all prime factors of the order of also divide the order of and is a verbal subgroup of .
Relation with other properties
- Central subgroup of finite group
- Cyclic normal subgroup of finite group
- Homocyclic normal subgroup of finite group