Conjugate-join-closed subgroup property

This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
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Definition

Symbol-free definition

A subgroup property $p$ is termed conjugate-join-closed if the join of a nonempty collection of conjugate subgroups satisfying $p$, also satisfies $p$. Note that any two subgroups in the collection must be conjugate; however, the collection need not include all members of that conjugacy class of subgroups.

Relation with other metaproperties

Stronger metaproperties

• Join-closed subgroup property
• Automorph-join-closed subgroup property

Weaker metaproperties

• Normal closure-closed subgroup property