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On groups in which subnormal subgroups of infinite rank are commensurable with some normal subgroup | ||
| International Journal of Group Theory | ||
| دوره 11، شماره 1، خرداد 2022، صفحه 37-42 اصل مقاله (187.72 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2021.127143.1671 | ||
| نویسندگان | ||
| Ulderico Dardano* ؛ Fausto De Mari | ||
| Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Via Cintia - Monte S. Angelo, I-80126 Napoli, Italy | ||
| چکیده | ||
| We study soluble groups $G$ in which each subnormal subgroup $H$ with infinite rank is commensurable with a normal subgroup, i.e. there exists a normal subgroup $N$ such that $H\cap N$ has finite index in both $H$ and $N$. We show that if such a $G$ is periodic, then all subnormal subgroups are commensurable with a normal subgroup, provided either the Hirsch-Plotkin radical of $G$ has infinite rank or $G$ is nilpotent-by-abelian (and has infinite rank). | ||
| کلیدواژه‌ها | ||
| transitivity؛ core-finite؛ normal-by-finite؛ close to normal | ||
| مراجع | ||
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[1] J. T. Buckley, J. C. Lennox, B. H. Neumann, H. Smith and J. Wiegold, Groups with all subgroups normal-by-finite, J. Austral. Math. Soc. Ser. A, 59 (1995) 384–398. [2] C. Casolo, Groups with finite conjugacy classes of subnormal subgroups, Rend. Sem. Mat. Univ. Padova, 81 (1989) 107–149. [3] C. Casolo, U. Dardano and S. Rinauro, Groups in which each subgroup is commensurable with a normal subgroup, J. Algebra, 496 (2018) 48–60. [4] U. Dardano and F. De Mari, Groups in which each subnormal subgroup is commensurable with some normal subgroup, J. Group Theory, https://doi.org/10.1515/jgth-2020-0076.
[5] U. Dardano and F. De Mari, On groups with all proper subgroups finite-by-abelian-by-finite, Arch. Math. (Basel), https://doi.org/10.1007/s00013-021-01580-6. [6] U. Dardano, F. De Mari and S. Rinauro, The weak minimal condition on subgroups which fail to be close to normal subgroups, J. Algebra, 560 (2020) 371–382. [7] U. Dardano, S. Rinauro, On soluble groups whose subnormal subgroups are inert, Int. J. Group Theory, 4 (2015) 17–24. [8] M. De Falco, F. de Giovanni, C. Musella, Y. P. Sysak, Groups of infinite rank in which normality is a transitive relation, Glasg. Math. J., 56 (2014) 387–393. [9] M. De Falco, F. de Giovanni, C. Musella, N. Trabelsi, Groups of infinite rank with finite conjugacy classes of subnormal subgroups, J. Algebra 431 (2015) 24–37. [10] F. De Mari, Groups with many modular or self-normalizing subgroups, to appear on Comm. Algebra, https: //doi.org/10.1080/00927872.2020.1870999. [11] S. Franciosi, F. de Giovanni, M. L. Newell, Groups whose subnormal subgroups are normal-by-finite, Comm. Algebra, 23 (1995) 5483–5497. [12] P. Hall, Some sufficient conditions for a group to be nilpotent, Illinois J. Math., 2 (1958) 787–801.
[13] B. H. Neumann, Groups with finite classes of conjugate subgroups, Math. Z., 63 (1955) 76–96.
[14] D. J. S. Robinson, Groups in which normality is a transitive relation, Proc. Cambridge Philos. Soc., 60 1964 21–38.
[15] D. J. S. Robinson, Finiteness conditions and generalized soluble groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, New York-Berlin, 1972. [16] D. J. S. Robinson, A Course in the Theory of Groups, Second edition. Graduate Texts in Mathematics, 80, Springer- Verlag, New York, 1996. | ||
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آمار تعداد مشاهده مقاله: 358 تعداد دریافت فایل اصل مقاله: 165 |
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