Join-transitively pronormal subgroup

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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

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 $H$ of a group $G$ is termed join-transitively pronormal if, for any pronormal subgroup $K$ of $G$, the join $\langle H, K \rangle$ 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

Relation with other properties

Stronger properties

• Normal subgroup
• Abnormal subgroup
• Weakly abnormal subgroup
• Upward-closed pronormal subgroup

Weaker properties

• Pronormal subgroup