Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896115 | Journal of Algebra | 2018 | 24 Pages |
Abstract
We give a classification and complete algebraic description of groups allowing only finitely many (left multiplication invariant) circular orders. In particular, they are all solvable groups with a specific semi-direct product decomposition. This allows us to also show that the space of circular orders of any group is either finite or uncountable. As a special case and first step, we show that the space of circular orders of an infinite Abelian group has no isolated points, hence is homeomorphic to a Cantor set.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Adam Clay, Kathryn Mann, Cristóbal Rivas,