# Subpronormal subgroup

From Groupprops

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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 subgroup property is a finitarily tautological subgroup property: when the ambient group is a finite group, the property is satisfied.

View other such subgroup properties

## Definition

### Definition with symbols

A subgroup of a group is termed **subpronormal** if there exists an ascending chain:

such that each is a pronormal subgroup of .

## Formalisms

### In terms of the subordination operator

This property is obtained by applying the subordination operator to the property: pronormal subgroup

View other properties obtained by applying the subordination operator

## Relation with other properties

### Stronger properties

- Pronormal subgroup
- Subnormal subgroup
- Subabnormal subgroup
- Submaximal subgroup
- Subgroup of finite index

## 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 transitiveABOUT 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