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Some Properties of Free Groups of Some Soluble Varieties of Groups
Author(s) -
Groves Daniel
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1017/s0024610701002022
Subject(s) - mathematics , central series , nilpotent , torsion (gastropod) , combinatorics , free group , pure mathematics , nilpotent group , group (periodic table) , chemistry , organic chemistry , biology , zoology
Let F be a free group, and let γ n ( F ) be the n th term of the lower central series of F . It is proved that F /[γ j ( F ), γ i ( F ), γ k ( F )] and F /[γ j ( F ), γ i ( F ), γ k ( F ), γ l ( 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.