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]
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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 of a group
is said to be intermediately automorph-conjugate if for any subgroup
of
such that
,
is an automorph-conjugate subgroup of
. In other words, for any automorphism
of
, there exists
such that
.
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
- Isomorph-free subgroup
- Intermediately isomorph-conjugate subgroup
- Intermediately characteristic subgroup
- Sylow subgroup