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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 of Group Theory – de Gruyter
Published: Jan 1, 1998
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