Solution to the Burnside Problem

Details Solution to the Burnside Problem Solution to the Burnside Problem

2008-03-11

arxiv.org/abs/0803.1612v1

Mathematics

Group Theory

14 pages. Most results here were contained in two earlier ArXiv papers. Although this paper is self contained, these previous

Scientific paper

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.

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