Join-transitively automorph-conjugate subgroup

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

Definition

Symbol-free definition

A subgroup of a group is termed join-transitively automorph-conjugate if its join with any automorph-conjugate subgroup is an automorph-conjugate subgroup.

Definition with symbols

A subgroup H of a group G is termed join-transitively automorph-conjugate if, for any automorph-conjugate subgroup K of G, the subgroup \langle H, K \rangle is also an automorph-conjugate subgroup.

Formalisms

In terms of the join-transiter

This property is obtained by applying the join-transiter to the property: automorph-conjugate subgroup
View other properties obtained by applying the join-transiter

Relation with other properties

Stronger properties

Weaker properties

Incomparable properties

Metaproperties

BEWARE! This section of the article uses terminology local to the wiki, possibly without giving a full explanation of the terminology used (though efforts have been made to clarify terminology as much as possible within the particular context)

Here is a summary:

Metaproperty name Satisfied? Proof Difficulty level (0-5) Statement with symbols
finite-join-closed subgroup property Yes (obvious) 0 Suppose H, K \le G are groups such that both H and K are automorph-conjugate in G. Then, \langle H, K \rangle is also automorph-conjugate in G.