Premium
Torsion in Certain Relatively Free Groups
Author(s) -
Tasić Vladimir,
Lee Michael Vaughan
Publication year - 1995
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/27.4.327
Subject(s) - mathematics , torsion (gastropod) , pure mathematics , variety (cybernetics) , statement (logic) , combinatorics , law , statistics , political science , medicine , surgery
We investigate the variety of groups determined by the identity[ [ x 1 , x 2 , … , x m ] , [ x m + 1 , x m + 2 , … , x m + n] ] = 1 , and show that relatively free groups in this variety are torsion free. This is done by proving the analogous statement for Lie rings. The proof yields an affirmative answer to a question of Djoković.