Abstract
Let G be a topological group. An element g∈G is called a topologically left Engel (t.l.e.) element iff the iterated commutators [...[[h,g],g]...,g] converge to 1 for every h∈G. This concept was introduced by V.P. Platonov, who asked various questions about these elements, e.g.: When do they form a subgroup? Especially, when does a group entirely consist of t.l.e. elements? What about the general properties of these elements?
The main part of this paper deals with Lie groups, where the t.l.e. elements can be described completely. With the aid of these results, answers to Platonov's questions are given for many classes of locally compact groups.
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Scheiderer, C. Topologisch linksengelsche Elemente. Manuscripta Math 49, 243–266 (1985). https://doi.org/10.1007/BF01215248
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DOI: https://doi.org/10.1007/BF01215248