Isomorph-commensurable 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]
This is a variation of isomorph-free subgroup|Find other variations of isomorph-free subgroup |

Definition

Symbol-free definition

A subgroup of a group is termed an isomorph-commensurable subgroup if it is commensurable with all subgroups of the group isomorphic to it.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Subgroup of finite group
Finite subgroup
Isomorph-free subgroup no other isomorphic subgroup

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Automorph-commensurable subgroup commensurable with all automorphic subgroups
Conjugate-commensurable subgroup commensurable with all conjugate subgroups