A note on conciseness of Engel words
Fernandez-Alcober, G. A., Moriagi, M. and Traustason, G., 2012. A note on conciseness of Engel words. Communications in Algebra, 40 (7), pp. 2570-2576.
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It is still an open problem to determine whether the n-th Engel word [x,_n y] is concise, that is, if for every group G such that the set of values e_n(G) taken by [x,_n y] on G is finite it follows that the verbal subgroup E_n(G) generated by e_n(G) is also finite. We prove that if e_n(G) is finite then [En_(G),G] is finite, and either G=[E_n(G),G] is locally nilpotent and E_n(G) is finite, or G has a finitely generated section that is an infinite simple n-Engel group. It follows that [x_n y] is concise if n is at most four.
|Creators||Fernandez-Alcober, G. A., Moriagi, M. and Traustason, G.|
|Departments||Faculty of Science > Mathematical Sciences|
|Publisher Statement||paper30.pdf: This is a preprint of an article submitted for consideration in the Communications in Algebra (forthcoming)[copyright Taylor & Francis]; Communications in Algebra is available online at: www.tandfonline.com|
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