Finite-p-potentially characteristic subgroup

From Groupprops
Jump to: navigation, search
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]

Statement

Suppose p is a prime number and G is a finite p-group (i.e., a group of prime power order). In other words, G is a group of prime power order. A subgroup H of G is termed a finite-p-potentially characteristic subgroup if there exists a finite p-group K containing G such that H is a characteristic subgroup of K.

Facts

Relation with other properties

The generalization of this property to finite groups, rather than just finite p-groups, is the property of being a finite-pi-potentially characteristic subgroup.

Stronger properties

Weaker properties