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 of a group is termed normal-potentially characteristic in if there exists a group containing such that:
- is a normal subgroup of .
- is a characteristic subgroup of .
Formalisms
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In terms of the upper-hook operator
Given two subgroup properties and , the upper-hook operator of and is defined as the following property : a subgroup of a group has property if there exists a group containing such that has property in and has property in .
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.