Classification of generalized torsion elements of order two in 3-manifold groups

2024/06/06 by Keisuke Himeno, Himeno, Keisuke, Kimihiko Motegi +3
Mathematics · #57K10 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2406.03754

openalex publication_date 2024/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a group and g a non-trivial element in G. If some non-empty finite product of conjugates of g equals to the identity, then g is called a generalized torsion element. The minimum number of conjugates in such a product is called the order of g. We will classify 3-manifolds M, each of whose fundamental group has a generalized torsion element of order two. Furthermore, we will classify such elements in π₁(M). We also prove that R-group and R-group coincide for 3-manifold groups, and classify 3-manifold groups which are R-groups (and hence R-groups).

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