Subabnormal subgroup

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 subabnormal if there exists an ascending chain:

$H=H_{0}\leq H_{1}\leq \ldots \leq H_{n}=G$

such that each $H_{i}$ is an abnormal subgroup of $G$.

Relation with other properties

Stronger properties

• Abnormal subgroup

Weaker properties

• Contranormal subgroup
• Subpronormal 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
ABOUT TRANSITIVITY: View a complete list of transitive subgroup properties|View a complete list of facts related to transitivity of subgroup properties |Read a survey article on proving transitivity