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

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