On the nature of finite groups

2004/08/16 by Aleksandr Golubchik, Golubchik, Aleksandr
Mathematics · #58D19 #FOS: Mathematics #Finite Group Theory Research #General Mathematics (math.GM) #Geometric and Algebraic Topology #Mathematics and Applications #math.GM #msc:58D19

paper · pdf · doi:10.48550/arxiv.math/0408202

4 pages, Latex2e

openalex publication_date 2004/08/16 · arxiv created 2004/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The reality of the difficulties in investigation of finite groups are considered. It is shown that the consideration of symmetry properties of the k-orbits that are obtained with an action of a finite group F=(V,⋅) on Cartesian power V^k gives a new view on the nature of groups and simplifies some difficult properties of groups. Using this representation it is obtained a simple proof of the W. Feit, J.G. Thompson theorem: Solvability of groups of odd order.

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