Translation-separable group

History
The notion of translation-separability was introduced, and used, by Gregory R. Conner in his paper Discreteness properties of translation numbers in solvable groups.

Symbol-free definition
A finitely generated group is said to be translation-separable or translation-proper if it satisfies the following equivalenyt conditions:


 * There exists a generating set with respect to which the set of translation numbers has zero as an isolated point. In other words, there is a generating set, and a positive real number $$\epsilon$$, such that there is no translation number betwee 0 and $$\epsilon$$.
 * For any generating set, the set of translation numbers has zero as an isolated point. In other words, for any generating set, and a positive real number $$\epsilon$$, such that there is no translation number betwee 0 and $$\epsilon$$.