# Join-transitively pronormal 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]

## Definition

### Symbol-free definition

A subgroup of a group is termed **join-transitively pronormal** if its join with any pronormal subgroup of the group is pronormal.

### Definition with symbols

A subgroup of a group is termed **join-transitively pronormal** if, for any pronormal subgroup of , the join is also pronormal.

## Formalisms

### In terms of the join-transiter

This property is obtained by applying the join-transiter to the property: pronormal subgroup

View other properties obtained by applying the join-transiter