2008/03/11 by S. Bachmuth, Seymour Bachmuth, Bachmuth, Seymour
Computer Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0803.1612
14 pages. Most results here were contained in two earlier ArXiv papers. Although this paper is self contained, these previous ones may be helpful
arxiv created 2008/03/11 · openalex publication_date 2008/03/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Burnside Problem asks whether a finitely generated group of exponent n is finite. We present a solution for 2-generator groups of prime power exponent. Results of P. Hall and G. Higman extends the finiteness conclusion to groups having composite exponents. Our main result, called the Generalized Burnside Theorem, is a solvability theorem that applies to a family of groups called GB (Generalized Burnside) groups that contain infinite as well as finite groups. The final section discusses the extension to k-generator groups although details are left for another time.