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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.

MSC: 22A05

Received: 02.02.2012
Revised: 21.09.2012

Language: English

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