Automorph-commensurable 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 an automorph-commensurable subgroup if it is commensurable with all its automorphic subgroups.

Definition with symbols

A subgroup of a group is termed an automorph-commensurable subgroup if, for any automorphism of , has finite index in both and .

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Characteristic subgroup
Finite subgroup
Subgroup of finite group
Subgroup of finite index
Isomorph-commensurable subgroup

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Conjugate-commensurable subgroup