FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2004, VOLUME 10, NUMBER 4, PAGES 15-22

Topological prime radical of a group

B. Bazigaran
S. T. Glavatsky
A. V. Mikhalev

Abstract

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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 $$h(G) is defined as the intersection of all closed prime normal subgroups of a topological group $G$. Its properties are investigated. In the second approach, we consider the set $$h'(G) of all topologically strictly Engel elements of a topological group $G$. Its properties are investigated. It is proved that $$h'(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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Last modified: April 14, 2005