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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2012, Number 3, Pages 38–44
(Mi basm327)
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This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 02.02.2012 Revised: 21.09.2012
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
Linking options:
https://www.mathnet.ru/eng/basm327 https://www.mathnet.ru/eng/basm/y2012/i3/p38
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Abstract page: | 211 | Full-text PDF : | 52 | References: | 44 | First page: | 1 |
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