Sub-central factor of normalizer

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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]

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Definition

Definition with symbols

A subgroup $H$ of a group $G$ is termed a sub-central factor of normalizer if there exists an ascending chain:

$H = H_0 \le H_1 \le \ldots \le H_n = G$

such that each $H_i$ is a central factor of normalizer of $H_{i+1}$.

Formalisms

In terms of the subordination operator

This property is obtained by applying the subordination operator to the property: central factor of normalizer
View other properties obtained by applying the subordination operator

Relation with other properties

Stronger properties

• Central factor of normalizer
  • Central factor
  • Self-normalizing subgroup

Metaproperties

Transitivity

This subgroup property is transitive: a subgroup with this property in a subgroup with this property, also has this property in the whole group.
ABOUT THIS PROPERTY: View variations of this property that are transitive | View variations of this property that are not transitive
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