Solution to the Burnside Problem
Abstract
The Burnside Problem asks whether a finitely generated group of exponent n is finite. We present a solution for 2generator 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 kgenerator groups although details are left for another time.
 Publication:

arXiv eprints
 Pub Date:
 March 2008
 DOI:
 10.48550/arXiv.0803.1612
 arXiv:
 arXiv:0803.1612
 Bibcode:
 2008arXiv0803.1612B
 Keywords:

 Mathematics  Group Theory
 EPrint:
 14 pages. Most results here were contained in two earlier ArXiv papers. Although this paper is self contained, these previous ones may be helpful