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Free products of circularly ordered groups with amalgamated subgroup. (English) Zbl 07174670
Summary: This paper gives necessary and sufficient conditions that the free product with amalgamation of circularly ordered groups admit a circular ordering extending the given orderings of the factors. Our result follows from establishing a categorical framework that allows the problem to be restated in terms of amalgamating certain left-ordered central extensions, where we are able to apply work of Bludov and Glass.
MSC:
20F60 Ordered groups (group-theoretic aspects)
08B25 Products, amalgamated products, and other kinds of limits and colimits
18A35 Categories admitting limits (complete categories), functors preserving limits, completions
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
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