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Exotic left orderings of the free groups from the Dehornoy ordering

2009/06/26 by Adam Clay, Clay, Adam
Computer Science · Mathematics · #06F15 #20E05 #20F36 #20F60 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:06F15 #msc:20E05 #msc:20F36 #msc:20F60 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0906.4997

8 pages, Proposition 3.2 has been removed due to an error in the proof. The main results of the paper are unchanged. Some typos corrected

openalex publication_date 2009/06/26 · arxiv created 2009/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the restriction of the Dehornoy ordering to an appropriate free subgroup of the three-strand braid group defines a left ordering of the free group on k generators, k>1, that has no convex subgroups.

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