Normal-potentially characteristic 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]
This term is related to: potentially characteristic subgroups characterization problem
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Definition

A subgroup H of a group K is termed normal-potentially characteristic in K if there exists a group G containing K such that:

Formalisms

BEWARE! This section of the article uses terminology local to the wiki, possibly without giving a full explanation of the terminology used (though efforts have been made to clarify terminology as much as possible within the particular context)

In terms of the upper-hook operator

Given two subgroup properties p and q, the upper-hook operator of p and q is defined as the following property r: a subgroup H of a group K has property r if there exists a group G containing K such that H has property p in G and K has property q in G.

The property of being semi-strongly potentially characteristic is thus obtained by applying the upper-hook operator to the properties characteristic subgroup and normal subgroup.

Relation with other properties

Stronger properties

Weaker properties