On locally graded groups with an Engel condition on infinite subsets

Authors
Longobardi, P
Citation
P. Longobardi, On locally graded groups with an Engel condition on infinite subsets, ARCH MATH, 76(2), 2001, pp. 88-90
Citations number
11
Categorie Soggetti
Mathematics
Journal title
ARCHIV DER MATHEMATIK
ISSN journal
0003889X → ACNP
Volume
76
Issue
2
Year of publication
2001
Pages
88 - 90
Database
ISI
SICI code
0003-889X(20010201)76:2<88:OLGGWA>2.0.ZU;2-4
Abstract
A group G is said to be in E-k* (k a positive integer), if every infinite s ubset of G contains a pair of elements that generate a k-Engel group. It is shown that a finitely generated locally graded group G in E-k* is a f inite-by- (k-Engel) group, in particular a finite extension of a k-Engel gr oup.