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Some Properties of Free Groups of Some Soluble Varieties of Groups

Authors:	Groves Daniel

Institution:	Department of Mathematics, University College Oxford OX1 4BH

Abstract:	Let F be a free group, and let ${gamma}$ _n(F) be the nth term of the lowercentral series of F. It is proved that F/ ${gamma}$ _j(F), ${gamma}$ _i(F), ${gamma}$ _k(F)]and F/ ${gamma}$ _j(F), ${gamma}$ _i(F), ${gamma}$ _k(F), ${gamma}$ _l(F)] are torsion free and residuallynilpotent for certain values of i, j, k and i, j, k, l, respectively.In the process of proving this, it is proved that the analogousLie rings are torsion free.

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