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  • 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 $E^*_4(G)$.

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A. Abdollahi , ‘Left 3-Engel elements in groups’, J. Pure Appl. Algebra 188 (2004), 16.

A. Abdollahi and H. Khosravi , ‘On the right and left 4-Engel elements’, Comm. Algebra 38 (2010), 933943.

A. Abdollahi and H. Khosravi , ‘Right 4-Engel elements of a group’, J. Algebra Appl. 9 (2010), 763769.

A. Abdollahi and F. G. Russo , ‘On a problem of P. Hall for Engel words’, Arch. Math. (Basel) 97 (2011), 407412.

G. A. Fernández-Alcober , M. Morigi and G. Traustason , ‘A note on conciseness of Engel words’, Comm. Algebra 40 (2012), 25702576.

G. A. Fernández-Alcober and P. Shumyatsky , ‘On groups in which commutators are covered by finitely many cyclic subgroups’, J. Algebra 319 (2008), 48444851.

G. Havas and M. R. Vaughan-Lee , ‘4-Engel groups are locally nilpotent’, Int. J. Algebra Comput. 15 (2005), 649682.

L.-C. Kappe , ‘Engel margins in metabelian groups’, Comm. Algebra 11 (1983), 165187.

T. K. Teague , ‘On the Engel margin’, Pacific J. Math. 50 (1974), 205214.

G. Traustason , ‘On 4-Engel groups’, J. Algebra 178 (1995), 414429.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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