Strongly translation-discrete group
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This term is related to: geometric group theory
View other terms related to geometric group theory | View facts related to geometric group theory
A finitely generated group is said to be strongly translation-discrete if it satisfies the following equivalent conditions:
- There exists a finite generating set such that the group is translation-separable with respect to that generating set, and further, for any , the number of conjugacy classes for which the translation number is , is finite.
- For every finite generating set of the group, the group is translation-separable with respect to that generating set, and further, for any , the number of conjugacy classes for which the translation number is , is finite.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|finitely generated free group||finitely generated free implies strongly translation-discrete|||FULL LIST, MORE INFO|
|finitely generated abelian group||finitely generated abelian implies strongly translation-discrete|||FULL LIST, MORE INFO|