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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.
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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 is an automorph-conjugate subgroup of K. In other words, for any automorphism σ of K, there exists 
such that σ(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 all properties obtained by applying the intermediately operator
Relation with other properties
Stronger properties
- Isomorph-free subgroup
- Intermediately isomorph-conjugate subgroup
- Intermediately characteristic subgroup
- Sylow subgroup
Weaker properties
- Intermediately automorph-conjugate subgroup of normal subgroup
- Weakly pronormal subgroup
- Polynormal subgroup
- Intermediately normal-to-characteristic subgroup
- Intermediately subnormal-to-normal subgroup
- Automorph-conjugate subgroup
Facts about Intermediately automorph-conjugate subgroupRDF feed
