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On the number of circular orders on a group. (arXiv:1704.06242v1 [math.GR])
来源于:arXiv
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. 查看全文>>