Conjugate-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


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

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

Weaker metaproperties