On residually finite groups in which commutators are Engel

Authors
Shumyatsky, P
Citation
P. Shumyatsky, On residually finite groups in which commutators are Engel, COMM ALGEB, 27(4), 1999, pp. 1937-1940
Citations number
7
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS IN ALGEBRA
ISSN journal
00927872 → ACNP
Volume
27
Issue
4
Year of publication
1999
Pages
1937 - 1940
Database
ISI
SICI code
0092-7872(1999)27:4<1937:ORFGIW>2.0.ZU;2-4
Abstract
Let k, n be positive integers, G a residually finite group such that [x(1), x(2),...,x(k)] is n-Engel for any x(1), x(2),..., x(k) is an element of G. We prove that gamma k(G) is locally nilpotent. For k = 1 this is a well-kn own result of J. Wilson.