naa a22 4500 51078223X CHVBK 20180411083251.0 cr unu---uuuuu 180411e20131101xx s 000 0 eng 10.1007/s11856-013-0041-8 doi (NATIONALLICENCE)springer-10.1007/s11856-013-0041-8 Nil-automorphisms of groups with residual properties [Elektronische Daten] [Carlo Casolo, Orazio Puglisi] Let G be any group and x an automorphism of G. The automorphism x is said to be nil if, for every g ∈ G, there exists n = n(g) such that [g, n x] = 1. If n can be chosen independently of g, we say that x is n-unipotent. A nil (resp. unipotent) automorphism x could also be seen as a left Engel element (resp. left n-Engel element) in the group G〈x〉. When G is a finite dimensional vector space, groups of unipotent linear automorphisms turn out to be nilpotent, so that one might ask to what extent this result can be extended to a more general setting. In this paper we study finitely generated groups of nil or unipotent automorphisms of groups with residual properties (e.g. locally graded groups, residually finite groups, profinite groups), proving that such groups are nilpotent. Hebrew University Magnes Press, 2013 Casolo Carlo Dipartimento di Matematica "U. Dini”, Università di Firenze, Viale Morgagni 67A, I-50134, Firenze, Italy aut Puglisi Orazio Dipartimento di Matematica "U. Dini”, Università di Firenze, Viale Morgagni 67A, I-50134, Firenze, Italy aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 91-110 0021-2172 198:1<91 2013 198 11856 https://doi.org/10.1007/s11856-013-0041-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-013-0041-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Casolo Carlo Dipartimento di Matematica "U. Dini”, Università di Firenze, Viale Morgagni 67A, I-50134, Firenze, Italy aut NATIONALLICENCE 700 1- Puglisi Orazio Dipartimento di Matematica "U. Dini”, Università di Firenze, Viale Morgagni 67A, I-50134, Firenze, Italy aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 91-110 0021-2172 198:1<91 2013 198 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer