Subgroup having a pronormalizer

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 a subgroup having a pronormalizer if $H$ has a pronormalizer in $G$: a subgroup $K$ of $G$ containing $H$ such that $H$ is pronormal in $K$, and if $H\leq L\leq G$ are such that $H$ is pronormal in $L$, then $L\leq K$.

Relation with other properties

Stronger properties

• Normal subgroup
• Subnormal subgroup
• Pronormal subgroup