Groups generated by two elliptic elements in PU(2,1)

2010/03/14 by Baohua Xie, Xie, Baohua, Yue-Ping Jiang +2
Mathematics · #Advanced Algebra and Geometry #Complex Variables (math.CV) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #math.CV

paper · pdf · doi:10.48550/arxiv.1003.2789

9 pages

arxiv created 2010/03/14 · openalex publication_date 2010/03/14 · arxiv updated 2010/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f and g be two elliptic elements in PU(2,1) of order m and n respectively, where m≥ n>2. We prove that if the distance δ(f,g) between the complex lines or points fixed by f and g is large than a certain number, then the group < f, g > is discrete nonelementary and isomorphic to the free product Z_m*Z_n.

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