Characteristic central subgroup

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristic subgroup and central subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

A subgroup $H$ of a group $G$ is termed a characteristic central subgroup if it satisfies both these conditions:

1. $H$ is a characteristic subgroup of $G$.
2. $H$ is a central subgroup of $G$, i.e., it is contained in the center of $G$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
characteristic subgroup of center	central subgroup that is characteristic as a subgroup of the center.	follows from center is characteristic and characteristicity is transitive
characteristic subgroup of abelian group				|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
characteristic subgroup
central subgroup
characteristic central factor
characteristic transitively normal subgroup
abelian characteristic subgroup
abelian normal subgroup