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arXiv · 1704.06242

On the number of circular orders on a group

Adam Clay·Kathryn Mann·Cristóbal Rivas
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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 orderings of an infinite Abelian group has no isolated points, hence is homeomorphic to a cantor set.

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Adam Clay, Kathryn Mann, Cristóbal Rivas. 2017-04-20. On the number of circular orders on a group. https://arxiv.org/abs/1704.06242

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