caa a22 4500 388046805 CHVBK 20180307125040.0 cr unu---uuuuu 161130e199802 xx s 000 0 eng 10.1017/S1446788700001324 doi S1446788700001324 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700001324 A note on Engel groups and local nilpotence [Elektronische Daten] This paper is concerned with the question of whether n-Engel groups are locally nilpotent. Although this seems unlikely in general, it is shown here that it is the case for the groups in a large class C including all residually soluble and residually finite groups (in fact all groups considered in traditional textbooks on group theory). This follows from the main result that there exist integers c(n), e(n) depending only on n, such that every finitely generated n-Engel group in the class C is both finite-of-exponent-e(n)-by-nilpotent-of-class≤c(n) and nilpotent-of-class≤c(n)-by-finite-of-exponent-e(n). Crucial in the proof is the fact that a finitely generated Engel group has finitely generated commutator subgroup. Copyright © Australian Mathematical Society 1998 20F45 nationallicence 20F19 nationallicence 20E10 nationallicence Burns R. G. Department of Mathematics Statistics York University North York Ontario, M3J 1P3 Canada e-mail Medvedev Yuri Department of Mathematics Statistics York University North York Ontario, M3J 1P3 Canada e-mail: rburns@mathstat.yorku.ca medvedev@mathstat. yorku.ca Journal of the Australian Mathematical Society Cambridge University Press 64/1(1998-02), 92-100 1446-7887 64:1<92 1998 64 JAZ https://doi.org/10.1017/S1446788700001324 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700001324 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Burns R. G. Department of Mathematics Statistics York University North York Ontario, M3J 1P3 Canada e-mail NATIONALLICENCE 700 1- Medvedev Yuri Department of Mathematics Statistics York University North York Ontario, M3J 1P3 Canada e-mail: rburns@mathstat.yorku.ca medvedev@mathstat. yorku.ca NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 64/1(1998-02), 92-100 1446-7887 64:1<92 1998 64 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge