Upward-closed transitively normal 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 an upward-closed transitively normal subgroup if every subgroup of the whole group containing it is a transitively normal subgroup of the whole group.

Definition with symbols

A subgroup $H$ of a group $G$ is termed an upward-closed transitively normal subgroup if, for every subgroup $K$ of $G$ containing $H$ and every normal subgroup $L$ of $K$, $L$ is normal in $G$.

Formalisms

In terms of the upward-closure operator

This property is obtained by applying the upward-closure operator to the property: transitively normal subgroup
View other properties obtained by applying the upward-closure operator