On profinite groups in which commutators are Engel

Authors
Shumyatsky, P
Citation
P. Shumyatsky, On profinite groups in which commutators are Engel, J AUS MAT A, 70, 2001, pp. 1-9
Citations number
18
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
ISSN journal
02636115 → ACNP
Volume
70
Year of publication
2001
Part
1
Pages
1 - 9
Database
ISI
SICI code
0263-6115(200102)70:<1:OPGIWC>2.0.ZU;2-M
Abstract
We show that if G is a finitely generated profinite group such that [x(1),x (2),...x(k)] is Engel for any x(1),x(2),...,x(k) is an element of G then ga mma (k)(G) is locally nilpotent, and if [x(1),x(2),...,x(k)] has finite ord er for any x(1),x(2),...,x(k) is an element of G then, under some additiona l assumptions, gamma (k)(G) is locally finite.