Conjugate-commensurable subgroup

Symbol-free definition
A subgroup of a group is termed conjugate-commensurable if it is commensurable with each of its defining ingredient::conjugate subgroups. Equivalently, its commensurator in the whole group is the whole group.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed a conjugate-commensurable subgroup if, for any $$g \in G$$, $$H \cap gHg^{-1}$$ has finite index in both $$H$$ and $$gHg^{-1}$$.