Commensurable subgroups
This article defines a symmetric relation on the collection of subgroups inside the same group.
Definition
Symbol-free definition
Two subgroups of a group are said to be commensurable if their intersection has finite index in both of them.
Definition with symbols
Two subgroups and of a group are said to be commensurable if both and are finite.
![{\displaystyle [H_{1}:H_{1}\cap H_{2}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf583be684b585b74b952e8d7c94fa86a33ce2be)
![{\displaystyle [H_{2}:H_{1}\cap H_{2}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c1488f76bfe9a39cc618780ffe31867128283feb)