Abstract
In this paper, we consider two approaches toward the definition of a topological prime radical of a topological group. In the first approach, the prime quasi-radical η(G) is defined as the intersection of all closed prime normal subgroups of a topological group G. Its properties are investigated. In the second approach, we consider the set η′(G) of all topologically strictly Engel elements of a topological group G. Its properties are investigated. It is proved that η′(G) is a radical in the class of all topological groups possessing a basis of neighborhoods of the identity element consisting of normal subgroups.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 15–22, 2004.
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Bazigaran, B., Glavatsky, S.T. & Mikhalev, A.V. Topological prime radical of a group. J Math Sci 140, 186–190 (2007). https://doi.org/10.1007/s10958-007-0415-8
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DOI: https://doi.org/10.1007/s10958-007-0415-8