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SOME PROPERTIES OF FREE GROUPS OF SOME SOLUBLE VARIETIES OF GROUPS

Published online by Cambridge University Press:  05 July 2001

DANIEL GROVES
DANIEL GROVES
Affiliation:
Department of Mathematics, University College, Oxford OX1 4BH
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Abstract

Let F be a free group, and let γn(F) be the nth term of the lower central series of F. It is proved that F/[γj(F), γi(F), γk(F)] and F/[γj(F), γi(F), γk(F), γl(F)] are torsion free and residually nilpotent for certain values of i, j, k and i, j, k, l, respectively. In the process of proving this, it is proved that the analogous Lie rings are torsion free.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 63 , Issue 3 , June 2001 , pp. 592 - 606
Copyright
The London Mathematical Society 2001

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