Skip to main content


  • FRANCESCO G. RUSSO (a1) (a2)

The present paper is related to some recent studies in Abdollahi and Russo [‘On a problem of P. Hall for Engel words’, Arch. Math. (Basel) 97 (2011), 407–412] and Fernández-Alcober et al. [‘A note on conciseness of Engel words’, Comm. Algebra 40 (2012), 2570–2576] on the position of the $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}n$ -Engel marginal subgroup $E^*_n(G)$ of a group $G$ , when $n=3,4$ . Describing the size of $E^*_n(G)$ for $n=3,4$ , we show some generalisations of classical results on the partial margins of $E^*_3(G)$ and $E^*_4(G)$ .

Hide All
[1]Abdollahi, A., ‘Left 3-Engel elements in groups’, J. Pure Appl. Algebra 188 (2004), 16.
[2]Abdollahi, A., ‘Engel elements in groups’, in: Groups St Andrews 2009 in Bath, LMS Lecture Notes 387 (Cambridge University Press, Cambridge, 2011), 94117.
[3]Abdollahi, A. and Khosravi, H., ‘On the right and left 4-Engel elements’, Comm. Algebra 38 (2010), 933943.
[4]Abdollahi, A. and Khosravi, H., ‘Right 4-Engel elements of a group’, J. Algebra Appl. 9 (2010), 763769.
[5]Abdollahi, A. and Russo, F. G., ‘On a problem of P. Hall for Engel words’, Arch. Math. (Basel) 97 (2011), 407412.
[6]Fernández-Alcober, G. A., Morigi, M. and Traustason, G., ‘A note on conciseness of Engel words’, Comm. Algebra 40 (2012), 25702576.
[7]Fernández-Alcober, G. A. and Shumyatsky, P., ‘On groups in which commutators are covered by finitely many cyclic subgroups’, J. Algebra 319 (2008), 48444851.
[8]Gupta, N. D. and Newman, M. F., ‘Third Engel groups’, Bull. Aust. Math. Soc. 40 (1989), 215230.
[9]Hall, P., ‘Verbal and marginal subgroups’, J. reine angew. Math. 182 (1940), 156157.
[10]Havas, G. and Vaughan-Lee, M. R., ‘4-Engel groups are locally nilpotent’, Int. J. Algebra Comput. 15 (2005), 649682.
[11]Heineken, H., ‘Engelsche Elemente der Länge drei’, Illinois J. Math. 5 (1961), 681707.
[12]Kappe, L.-C., ‘Engel margins in metabelian groups’, Comm. Algebra 11 (1983), 165187.
[13]Kappe, W. P., ‘Some subgroups defined by identities’, Illinois J. Math. 47 (2003), 317326.
[14]Kappe, L.-C. and Kappe, W. P., ‘On three-Engel groups’, Bull. Aust. Math. Soc. 7 (1972), 391405.
[15]Newell, M., ‘On right Engel elements of length three’, Proc. Roy. Irish Acad. Sect. A 96 (1996), 1724.
[16]Nickel, W., ‘Some groups with right Engel elements’, in: Groups St. Andrews 1997 in Bath, LMS Lecture Notes 261 (Cambridge University Press, Cambridge, 1999), 571578.
[17]Segal, D., ‘Words: notes on verbal width in groups’, LMS Lecture Notes 361 (Cambridge University Press, Cambridge, 2009).
[18]Stroud, P., ‘On a property of verbal and marginal subgroups’, Proc. Camb. Philos. Soc. 61 (1965), 4148.
[19]Teague, T. K., ‘On the Engel margin’, Pacific J. Math. 50 (1974), 205214.
[20]The GAP Group, GAP—Groups, Algorithms and Programming (version 4.4, available at, 2005).
[21]Traustason, G., ‘On 4-Engel groups’, J. Algebra 178 (1995), 414429.
[22]Traustason, G., ‘Locally nilpotent 4-Engel groups are Fitting groups’, J. Algebra 279 (2003), 727.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

MSC classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 12 *
Loading metrics...

Abstract views

Total abstract views: 122 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 16th July 2018. This data will be updated every 24 hours.