2017/04/20 by Clay, Adam, Mann, Kathryn, Rivas, Cristóbal
#06F15 #20F60 #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1704.06242
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.