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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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[1] R. Baer, Endlichkeitskriterien für Kommutatorgruppen, Math. Ann., 124 (1952) 161–177.
[2] G. Busetto, Proprietà di immersione dei sottogruppi modulari localmente ciclici nei gruppi, Rend. Sem. Mat. Univ. Padova, 63 (1980) 269–284. [3] M. De Falco, F. de Giovanni and C. Musella, The Schur property for subgroup lattices of groups, Arch. Math. (Basel), 91 (2008) 97–105. [4] M. De Falco, F. de Giovanni and C. Musella, Modular chains in infinite groups, Arch. Math. (Basel), 117 (2021) 601–612. [5] P. Hall, Finite-by-nilpotent groups, Proc. Cambridge Philos. Soc., 52 (1956) 611–616.
[6] N. S. Hekster, On the structure of n-isoclinism classes of groups, J. Pure Appl. Algebra, 40 (1986) 63–85.
[7] N. Ito, Note on (LM)-groups of finite orders, Kodei Math. Sem. Rep., (1951) 1–6.
[8] K. Iwasawa, On the structure of infinite M -groups, Jap. J. Math., 18 (1943) 709–728.
[9] P. G. Kontorovič and B. I. Plotkin, Lattices with an additive basis, Mat. Sb., 35 (1954) 187–192.
[10] O. Ore, Structures and group theory II, Duke Math. J., 4 (1938) 247–269.
[11] E. Previato, Una caratterizzazione reticolare dei gruppi risolubili finitamente generati, Ist. Veneto Sci. Lett. Arti Atti Cl. Sci. Fis. Mat. Natur., 136 (1978) 7–11. [12] R. Schmidt, Eine verbandstheoretische Charakterisierung der aufl´’osbaren und der öberauflösbaren endlichen Grup- pen, Archiv Math., 19 (1968) 449–452. [13] R. Schmidt, Modulare Untergruppen endlicher Gruppen, Illinois J. Math., 13 (1969) 358–377.
[14] R. Schmidt, Endliche Gruppen mit vielen modularen Untergruppen, Abh. Math. Se. Univ. Hamburg, 34 (1970) 115–125. [15] R. Schmidt, Gruppen mit modularem Untergruppenverband, Arch. Math. (Basel), 46 (1986) 118–124.
[16] R. Schmidt, Subgroup Lattices Of Groups, De Gruyter Expositions in Mathematics, 14, Walter de Gruyter & Co., Berlin, 1994. [17] R. Schmidt, Finite groups with modular chains, Colloquium Math., 131 (2013) 195–208.
[18] R. Schmidt, Lattice-theoretic characterizations of classes of groups, Integrable systems and algebraic geometry, 2, 367–382, London Math. Soc. Lecture Note Ser., 459, Cambridge Univ. Press, Cambridge, 2020. [19] I. Schur, Über die Darstellung der endlichen Gruppen durch gebrochene linear Substitutionen, J. Reine Angew. Math., 127 (1904) 20–50. [20] S. Stonehewer, Permutable subgroups of some finite p-groups, J. Austral. Math. Soc., 16 (1973) 90–97.
[21] G. Zacher, Una relazione di normalità sul reticolo dei sottogruppi di un gruppo, Ann. Mat. Pura Appl., 131 (1982) 57–73. [22] G. Zacher, Reticoli di sottogruppi normali e struttura normale di un gruppo, Ist. Veneto Sci. Lett. Arti Atti Cl. Sci. Fis. Mat. Natur., 157 (1999) 37–41. | ||
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