Intermediately automorph-conjugate subgroup

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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]


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

Definition

Symbol-free definition

A subgroup of a group is said to be intermediately automorph-conjugate if it is an automorph-conjugate subgroup in every intermediate subgroup (viz, every subgroup of the whole group containing it).

Definition with symbols

A subgroup H of a group G is said to be intermediately automorph-conjugate if for any subgroup K of G such that H \le K, H is an automorph-conjugate subgroup of K. In other words, for any automorphism \sigma of K, there exists g \in K such that \sigma(H) = gHg^{-1}.

Formalisms

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)

In terms of the intermediately operator

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

In terms of the intermediately operator

This property is obtained by applying the intermediately operator to the property: weakly procharacteristic subgroup
View other properties obtained by applying the intermediately operator

Relation with other properties

Stronger properties

Weaker properties