Properties of covers in the lattice of group topologies for nilpotent groups (Q2874210)
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scientific article; zbMATH DE number 6251556
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Properties of covers in the lattice of group topologies for nilpotent groups |
scientific article; zbMATH DE number 6251556 |
Statements
29 January 2014
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nilpotent group
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group topology
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lattice of group topologies
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unrefinable chains
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coatom
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infimum of group topologies
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Properties of covers in the lattice of group topologies for nilpotent groups (English)
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The author constructs a nilpotent group and group topologies \(\mathcal T_1\) and \(\mathcal T_2\) on it such that between \(\mathcal T_1\) and \(\inf\{\mathcal T_1,\mathcal T_2\}\) there exists a chain of group topologies isomorphic to \(\mathbb Z\) as an ordered set. Related results on lattices of group topologies on a nilpotent group have been obtained in [the author, Bul. Acad. Ştiinţe Repub. Mold., Mat. 2010, No. 2(63), 3--19 (2010; Zbl 1204.22001)].
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