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Topological prime radical of a group
- Source :
- Journal of Mathematical Sciences. 140:186-190
- Publication Year :
- 2007
- Publisher :
- Springer Science and Business Media LLC, 2007.
-
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.
Details
- ISSN :
- 15738795 and 10723374
- Volume :
- 140
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Sciences
- Accession number :
- edsair.doi...........c6b18efea56e430e5cbc006520888f5b