Groups with the real chain condition on non-pronormal subgroups

Dardano, Ulderico; De Mari, Fausto

doi:10.22108/ijgt.2023.138453.1858

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	Groups with the real chain condition on non-pronormal subgroups
International Journal of Group Theory
مقاله 3، دوره 14، شماره 1، خرداد 2025، صفحه 9-18 اصل مقاله (415.55 K)
نوع مقاله: Ischia Group Theory 2022
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.138453.1858
نویسندگان
Ulderico Dardano^* ¹؛ Fausto De Mari²
¹Dipartimento di Matematica e Applicazioni “R.Caccioppoli”, Università di Napoli “Federico II”, Via Cintia - Monte S. Angelo, I-80126 Napoli, Italy
²Università di Napoli “Federico II”, I-80126 Napoli, Italy
چکیده
It is shown that a generalised radical group has no chain of non-pronormal subgroups with the same order type as the set $\mathbb{R}$ of the real numbers if and only if either the group is minimax or all subgroups are pronormal.
کلیدواژه‌ها
Pronormal subgroup؛ minimax group؛ weak chain condition؛ deviation

مراجع
[1] U. Dardano and F. De Mari, A real chain condition for groups, submitted. https://doi.org/10.48550/arXiv.2307.07639 [2] M. R. Dixon, Sylow theory, formations and Fitting classes in locally finite groups, Series in Algebra, 2, World Scientific Publishing Co., Inc., River Edge, NJ, 1994. https://doi.org/10.1142/2386. [3] M. R. Dixon, M. J. Evans and H. Smith, Locally soluble-by-finite groups with the weak minimal condition on non-nilpotent subgroups, J. Algebra, 249 (2002) 226–246. [4] M. R. Dixon and I. Y. Subbotin, Groups with finiteness conditions on some subgroup system: a contemporary stage, Algebra Discrete Math., 4 (2009) 29–54. [5] F. de Giovanni, L. A. Kurdachenko and A. Russo, Groups with pronormal deviation, J. Algebra, 613 (2023) 32–45. [6] F. de Giovanni and G. Vincenzi, Some topics in the theory of pronormal subgroups of groups, Topics in infinite groups, Quad. Mat., 8, Dept. Math., Seconda Univ. Napoli, Caserta, 2001 175–202. [7] F. de Giovanni and G. Vincenzi, Groups satisfying the minimal condition on non-pronormal subgroup, Boll. Un. Mat. Ital. A (7), 9 (1995) 185–194. [8] F. de Giovanni and G. Vincenzi, Pronormality in infinite groups, Math. Proc. R. Ir. Acad., 100A (2000) 189–203. [9] N. F. Kuzennyı̆ and I. Ya. Subbotin, Groups in which all subgroups are pronormal, Ukrainian Math. J., 39 (1987) 251–254. [10] J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, John Eiley and Sons, Chichester, 1988. [11] T. A. Peng, Finite groups with pronormal subgroups, Proc. Amer. Math. Soc., 20 (1969) 232–234. [12] D. J. S. Robinson, Groups in which normality is a transitive relation, Proc. Cambridge Philos. Soc., 60 (1964) 21–38. [13] D. J. S. Robinson, Finiteness conditions and generalized soluble groups, Springer, Berlin-New York, 1972. [14] D. J. S. Robinson, A course in the theory of groups, Springer, Berlin-New York, 1996. [15] A. V. Tushev, On deviation in groups, Illinois J. Math., 47 (2003) 539–550. [16] G. Vincenzi, Groups with dense pronormal subgroups, Ricerche Mat., 40 (1991) 75–79. [17] G. Vincenzi, Groups satisfying the maximal condition on non-pronormal subgroups, Algebra Colloq., 5 (1998) 121–134. [18] D. I. Zaicev, On the theory of minimax groups, Ukrainian Math. J., 23 (1971) 536–542.
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Groups with the real chain condition on non-pronormal subgroups