Normalizing join-closed subgroup property

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Normalizing join-closed subgroup property, all facts related to Normalizing join-closed subgroup property) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
View a complete list of subgroup metaproperties
View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

Definition

A subgroup property $p$ is termed normalizing join-closed if whenever $H,K\leq G$ are subgroups satisfying property $p$ such that $K$ is contained in the normalizer $N_{G}(H)$, the product of subgroups $HK$ (which is the same as the join of subgroups $\langle H,K\rangle$) also satisfies property $p$.

Relation with other metaproperties

Stronger metaproperties

• Join-closed subgroup property
• Finite-join-closed subgroup property