Conjugate-commensurable subgroup: Difference between revisions
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A subgroup of a group is termed '''conjugate-commensurable''' if it is [[defining ingredient::commensurable subgroups|commensurable]] with | A subgroup of a group is termed '''conjugate-commensurable''' if it is [[defining ingredient::commensurable subgroups|commensurable]] with each of its [[defining ingredient::conjugate subgroups]]. | ||
===Definition with symbols=== | ===Definition with symbols=== | ||
Revision as of 22:50, 16 January 2010
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]
This is a variation of normal subgroup|Find other variations of normal subgroup | Read a survey article on varying normal subgroup
Definition
Symbol-free definition
A subgroup of a group is termed conjugate-commensurable if it is commensurable with each of its conjugate subgroups.
Definition with symbols
A subgroup of a group is termed a conjugate-commensurable subgroup if, for any , 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 |
|---|---|---|---|---|
| Normal subgroup | |FULL LIST, MORE INFO | |||
| Subgroup of finite group | ||||
| Finite subgroup | ||||
| Subgroup of finite index | |FULL LIST, MORE INFO | |||
| Nearly normal subgroup | ||||
| Isomorph-commensurable subgroup | commensurable with every isomorphic subgroup | |||
| Automorph-commensurable subgroup | commensurable with every automorphic subgroup |