By V. A. Krechmar

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2, London Math. Soc. , vol. 212, Cambridge Univ. Press, Cambridge, 1995, pp. 567-585. Efim I. Zel'manov, More on Burnside's problem, Combinatorial and geometric group theory (Edinburgh, 1993), London Math. Soc. , vol. 204, Cambridge Univ. Press, Cambridge, 1995, pp. 314-321. Efim I. Zel'manov, Talk at the ESF conference on algebra and discrete mathematics "Group Theory: from Finite to Infinite", Castelvecchio Pascoli, 13-18 July 1996. Efim I. Zel'manov, On the restricted Burnside problem, Fields Medallists' lectures, World Sci.

Put (6 • l)(i) = t'o.. t'n. Then t'o is determined by l(t) and equals to > t\. As —1 is compatible with (b • l)(t), we must have t[ = t0. Thus e(l(t)) = l(t) starts by (to > h) • t0, and b(l(t)) = (b • l)(t) starts by (t0 > t\) • to as well. Now, ±1 does not occur in b, but ±2 does. Define c to be the shortest terminating factor of 6 which contains all occurences of +2 and —2. Then c ^ e, but the induction assumption implies c = i = e, a contradiction. Let us now consider (ii). 4, the term t^, k e {1,2}, depends only upon bk.

Small. [HB82] Bertram Huppert and Norman Blackburn, Finite groups II, Springer-Verlag, Berlin, 1982, AMD, 44. [Jac41] Nathan Jacobson, Restricted Lie algebras of characteristic p, Trans. Amer. Math. Soc. 50 (1941), 15-25. [Jac62] Nathan Jacobson, Lie algebras, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962, Interscience Tracts in Pure and Applied Mathematics, No. 10. 80] [Kal46] [Kes59] [KLP97] [Koc70] [Kou98] [Laz53] [Laz65] [Leo98] [LG94] [LM91] [Mag40] [Mei54] [Mil68] [MZ99] [Pas79] [Pman77] [Pet93] [Qui68] [Roz96a] [Roz96b] L Bartholdi and R I Grigorchuk Stephen A.

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