On the Equationally Artinian Groups

In this article, we study the property of being equationally Artinian in groups. We define the radical topology corresponding to such groups and investigate the structure of irreducible closed sets of these topologies. We prove that a finite extension of an equationally Artinian group is again equat...

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Bibliographic Details
Published in:Journal of Siberian Federal University. Mathematics & Physics 2020-01, Vol.13 (5), p.583-595
Main Authors: Shahryari, Mohammad, Tayyebi, Javad
Format: Article
Language:English
Subjects:
Group theory
Quotients
Subgroups
Topology
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Summary:In this article, we study the property of being equationally Artinian in groups. We define the radical topology corresponding to such groups and investigate the structure of irreducible closed sets of these topologies. We prove that a finite extension of an equationally Artinian group is again equationally Artinian. We also show that a quotient of an equationally Artinian group of the form G[t] by a normal subgroup which is a finite union of radicals, is again equationally Artnian. A necessary and sufficient condition for an Abelian group to be equationally Artinian will be given as the last result. This will provide a large class of examples of equationally Artinian groups
ISSN:1997-1397
2313-6022
DOI:10.17516/1997-1397-2020-13-5-583-595