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On Zel'manov's solution of the restricted Burnside problem

On Zel'manov's solution of the restricted Burnside problem Abstract. e give n outline of the min steps in el9mnov9s solution of the restrited furnE side prolemF e show how one of the key steps n e simpli®ed y using the multiliner identities stis®ed y the ssoited vie rings of groups of primeEpower exponentF 1 Introduction In 1989 Zel'manov [10], [11] solved the restricted Burnside problem by proving that the orders of all ®nite m-generator groups of exponent n are bounded above by a function of m and n. Zel'manov's solution relies on a reduction to groups of primepower exponent which is due to Hall and Higman [2]. They proved that if n k k k p1 1 p2 2 F F F pr r , then there is a bound on the orders of ®nite m-generator groups of exponent n (for all m) provided there is a bound on the orders of ®nite m-generator groups of exponent piki for all i 1Y 2Y F F F Y r and for all m. Kostrikin [3], [4] solved the restricted Burnside problem for prime exponent in 1959, but it was a further 30 years before Zel'manov completed the solution by proving that there is a bound on the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Group Theory de Gruyter

On Zel'manov's solution of the restricted Burnside problem

Journal of Group Theory , Volume 1 (1) – Jan 1, 1998

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References (12)

Publisher
de Gruyter
Copyright
Copyright © 1998 by the
ISSN
1433-5883
eISSN
1435-4446
DOI
10.1515/jgth.1998.003
Publisher site
See Article on Publisher Site

Abstract

Abstract. e give n outline of the min steps in el9mnov9s solution of the restrited furnE side prolemF e show how one of the key steps n e simpli®ed y using the multiliner identities stis®ed y the ssoited vie rings of groups of primeEpower exponentF 1 Introduction In 1989 Zel'manov [10], [11] solved the restricted Burnside problem by proving that the orders of all ®nite m-generator groups of exponent n are bounded above by a function of m and n. Zel'manov's solution relies on a reduction to groups of primepower exponent which is due to Hall and Higman [2]. They proved that if n k k k p1 1 p2 2 F F F pr r , then there is a bound on the orders of ®nite m-generator groups of exponent n (for all m) provided there is a bound on the orders of ®nite m-generator groups of exponent piki for all i 1Y 2Y F F F Y r and for all m. Kostrikin [3], [4] solved the restricted Burnside problem for prime exponent in 1959, but it was a further 30 years before Zel'manov completed the solution by proving that there is a bound on the

Journal

Journal of Group Theoryde Gruyter

Published: Jan 1, 1998

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