Transfer-closed 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

A subgroup $H$ of a group $G$ is termed transfer-closed pronormal if, for any subgroup $K$ of $G$, $H \cap K$ is a pronormal subgroup of $K$.

Formalisms

In terms of the transfer condition operator

This property is obtained by applying the transfer condition operator to the property: pronormal subgroup
View other properties obtained by applying the transfer condition operator

Relation with other properties

Stronger properties

• Hereditarily pronormal subgroup
• Normal subgroup

Weaker properties

• Pronormal subgroup