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IMI/Publicaţii/BASM/Ediţii/BASM n.3 (70), 2012/

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

Authors: Arnautov Vladimir
Keywords: Nilpotent group, group topology, lattice of group topologies, unrefinable chains, coatom, infimum of group topologies.

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.

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