Conjugacy classes of groups of prime order in\n \PGL_k+1(\ℂ)

2020/11/22 by Andrea Marinatto, Marinatto, Andrea
Mathematics · #14L35 (Primary) #14N99 (Secondary) #20E45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2011.11046

openalex publication_date 2020/11/22 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Let \ℂ be the field of complex numbers. Let k be natural number\nwith k \≥ 2 and let p be a rational prime. In this paper we count the\nnumber of conjugacy classes of admissible cyclic subgroups of\n\PGL_k+1(\ℂ) of order p, where with admissible we intend\nthose finite subgroups that can be contained in the automorphism group of a set\nof points in \ℙ^k(\ℂ) in general position and of cardinality\nn\≥ k+3. We also describe a kind of association between the conjugacy\nclasses of these groups and show a beautiful relation connecting this type of\nassociation and the association between point sets.\n

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