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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, Number 3, Pages 38–44 (Mi basm327)  

Properties of covers in the lattice of group topologies for nilpotent groups

V. I. Arnautov

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5, Academiei str., Chişinău, MD-2028, Moldova

Abstract: A nilpotent group $\widehat G$ and two group topologies $\widehat\tau"$ and $\widehat\tau*$ on $\widehat G$ are constructed such that $\widehat\tau*$ is a coatom in the lattice of all group topologies of the group $\widehat G$ and such that between $\inf\{\widehat\tau",\widehat\tau_d\}$ and $\inf\{\widehat\tau",\widehat\tau*\}$ there exists an infinite chain of group topologies.

Keywords and phrases: nilpotent group, group topology, lattice of group topologies, unrefinable chains, coatom, infimum of group topologies.

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Document Type: Article
MSC: 22A05
Received: 02.02.2012
Revised: 21.09.2012
Language: English

Citation: V. I. Arnautov, “Properties of covers in the lattice of group topologies for nilpotent groups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, no. 3, 38–44

Citation in format AMSBIB
\Bibitem{Arn12}
\by V.~I.~Arnautov
\paper Properties of covers in the lattice of group topologies for nilpotent groups
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2012
\issue 3
\pages 38--44
\mathnet{http://mi.mathnet.ru/basm327}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3155841}


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