Some properties of free groups of some soluble varieties of groups

Authors
Groves, D
Citation
D. Groves, Some properties of free groups of some soluble varieties of groups, J LOND MATH, 63, 2001, pp. 592-606
Citations number
16
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
ISSN journal
00246107 → ACNP
Volume
63
Year of publication
2001
Part
3
Pages
592 - 606
Database
ISI
SICI code
0024-6107(200106)63:<592:SPOFGO>2.0.ZU;2-#
Abstract
Let F be a free group, and let gamma (n)(F) be the nth term of the lower ce ntral 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 t orsion 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 analo gous Lie rings are torsion free.