On some new developments in the theory of subgroup lattices of groups
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| Titel: | On some new developments in the theory of subgroup lattices of groups |
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| Autoren: | Maria De Falco, Carmela Musella |
| Quelle: | International Journal of Group Theory, Vol 12, Iss 3, Pp 153-162 (2023) |
| Verlagsinformationen: | University of Isfahan, 2023. |
| Publikationsjahr: | 2023 |
| Bestand: | LCC:Mathematics |
| Schlagwörter: | modular lattice, permodular subgroup, permodular chain, Mathematics, QA1-939 |
| Beschreibung: | A rather natural way for trying to obtain a lattice-theoretic characterization of a class of groups ${\mathcal X}$ is to replace the concepts appearing in the definition of ${\mathcal X}$ by lattice-theoretic concepts. The first to use this idea were Kontorovi\v{c} and Plotkin who in 1954 introduced the notion of modular chain in a lattice, as translation of a central series of a group, to determine a lattice-theoretic characterization of the class of torsion-free nilpotent groups. The aim of this paper is to present a recent application of this translation method to some generalized nilpotency properties. |
| Publikationsart: | article |
| Dateibeschreibung: | electronic resource |
| Sprache: | English |
| ISSN: | 2251-7650 2251-7669 |
| Relation: | https://ijgt.ui.ac.ir/article_26618_4fa5889b4b31542b0c65fb633b016ce6.pdf; https://doaj.org/toc/2251-7650; https://doaj.org/toc/2251-7669 |
| DOI: | 10.22108/ijgt.2022.132076.1771 |
| Zugangs-URL: | https://doaj.org/article/e845c0213481481baa75f5034ec1b1c4 |
| Dokumentencode: | edsdoj.845c0213481481baa75f5034ec1b1c4 |
| Datenbank: | Directory of Open Access Journals |
Nájsť tento článok vo Web of Science | Abstract: | A rather natural way for trying to obtain a lattice-theoretic characterization of a class of groups ${\mathcal X}$ is to replace the concepts appearing in the definition of ${\mathcal X}$ by lattice-theoretic concepts. The first to use this idea were Kontorovi\v{c} and Plotkin who in 1954 introduced the notion of modular chain in a lattice, as translation of a central series of a group, to determine a lattice-theoretic characterization of the class of torsion-free nilpotent groups. The aim of this paper is to present a recent application of this translation method to some generalized nilpotency properties. |
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| ISSN: | 22517650 22517669 |
| DOI: | 10.22108/ijgt.2022.132076.1771 |