The k-orbit theory and Fein-Kantor-Schacher Theorem

2005/02/23 by Aleksandr Golubchik, Golubchik, Aleksandr
Mathematics · #20C99 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #General Mathematics (math.GM) #Geometric and Algebraic Topology #math.GM #msc:20C99

paper · pdf · doi:10.48550/arxiv.math/0502490

6 pages, Latex2e

openalex publication_date 2005/02/23 · arxiv created 2005/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By the investigation of k-orbits symmetry properties it is obtained a simple proof of the B. Fein, W. M. Kantor and M. Schacher Theorem: any transitive permutation group contains a non-trivial fixed-point-free prime-power element. Key words: k-orbits, partitions, permutations, symmetry, groups

Related

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• On the polycirculant conjecture
• Extended Orbits-Fixedpoints Relations
• Permutation Groups and Orbits on Power Sets
• Finite Permutation Groups with Few Orbits Under the Action on the Power Set