Geodesic
Topological prime radical of a~group
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 15-22

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In this paper, we consider two approaches for the definition of a topological prime radical of a topological group. In the first approach, the prime quasi-radical $\eta(G)$ 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 $\eta'(G)$ of all topologically strictly Engel elements of a topological group $G$. Its properties are investigated. It is proved that $\eta'(G)$ 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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     title = {Topological prime radical of a~group},
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B. Bazigaran; S. T. Glavatskii; A. V. Mikhalev. Topological prime radical of a~group. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 15-22. http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a1/