Topological prime radical of a group |
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Authors: | B Bazigaran S T Glavatsky A V Mikhalev |
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Institution: | (1) Moscow State University, Russia |
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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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