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On some new developments in the theory of subgroup lattices of groups | ||
| International Journal of Group Theory | ||
| مقاله 24، دوره 12، شماره 3، آذر 2023، صفحه 153-162 اصل مقاله (391.45 K) | ||
| نوع مقاله: Ischia Group Theory 2020/2021 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2022.132076.1771 | ||
| نویسندگان | ||
| Maria De Falco؛ Carmela Musella* | ||
| Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II Napoli, Italy | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| modular lattice؛ permodular subgroup؛ permodular chain | ||
| مراجع | ||
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