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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

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

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.

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