Normalizing join-closed subgroup property

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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 \le 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