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Journal of Lie Theory 33 (2023), No. 1, 079--091 Copyright Heldermann Verlag 2023 Engel Marginal Subgroups in Pro-Lie Groups Yanga Bavuma Department of Mathematical Sciences, University of South Africa, Pretoria, South Africa yangabavuma@gmail.com Francesco G. Russo (1) Department of Mathematics and Applied Mathematics, University of Cape Town, South Africa (2) Department of Mathematics and Applied Mathematics, University of the Western Cape, Bellville, South Africa francescog.russo@yahoo.com The position of the n-Engel marginal and verbal subgroups is placed between appropriate terms of the (upper or lower) central series of an abstract group, when n is small enough. In case of compact (Hausdorff) groups, the presence of a topological structure allows us to consider larger values of n, again controlling very well the position of these subgroups with respect to the terms of the central series. We observe a similar behaviour in the wider context of pro-Lie groups. Keywords: Topological groups, Engel words, pro-Lie groups, nilpotent groups. MSC: 22E20, 22E25, 22A05, 22C05. [ Fulltext-pdf (127 KB)] for subscribers only. |