On the classes of finite groups defined by the systems of generalized subnormal subgroups
Abstract
The canonical locals definitions of the classes of groups defined by the systems of generalized subnormal subgroups in the case when these classes are local are constructed in the paper. Conditions are found under which a class of groups defined by a system of generalized subnormal subgroups is a Fitting formation.
Supporting agencies: The work was carried out with the financial support of a grant from the Ministry of Education for doctoral students, graduate students, and students (No. 20240567)
References
1. Vasil’ev A. F, Vasil’eva T. I., Tyutyanov V. N. On the finite groups of supersoluble type. Sib. Math. J., 2010, vol. 51, no. 6, pp. 1004–1012.
2. Monakhov V. S., Kniahina V. N. Finite groups with P-subnormal subgroups. Ricerche mat. 2013, vol. 62, pp. 307–322.
3. Hawkes T. O. On formation subgroups of a finite soluble group. J. London Math. Soc., 1969, vol. 4, pp. 243–250.
4. Shemetkov L. A. Formations of finite groups. Moscow, Nauka, 1978. 272 p. (in Russian).
5. Kamornikov S. F., Selkin M. V. Subgroups functors and classes of finite groups. Minsk, Belaruskaya navuka, 2003. 254 p. (in Russian).
6. Ballester-Bollinches A., Ezquerro L. M. Classes of Finite Groups. Netherlands, Springer, vol. 584 of Math. Appl., 2006. 385 p.
7. Vasil’ev A. F., Vasilyeva T. I. On finite groups with generally subnormal Sylow subgroups. Probl. Fiz. Mat. Tekh., 2011, no. 4(9), pp. 86–91 (in Russian).
8. Semenchuk V. N. Shevchuk, S. N. Characterization of classes of finite groups with the use of generalized subnormal Sylow subgroups. Math. Notes, 2011, vol. 89, no. 1, pp. 117–120.
9. Vasil’eva T. I., Koranchuk, A. G. Finite Groups with Subnormal Residuals of Sylow Normalizers. Sib. Math. J., 2022, vol. 63, no. 4, pp. 670–676.
10. Monakhov V. S., Sokhor I. L. On groups with formational subnormal Sylow subgroups. J. Group Theory, 2018, vol. 21, pp. 273–287.
11. Guo W., Skiba A. N. Finite groups whose n-maximal subgroups are σ-subnormal. Sci. China Math., 2019, vol. 62, no. 7, pp. 1355–1372.
12. Vasil’ev A. F., Vasil’eva T. I., Vegera A. S. Finite groups with generalized subnormal embedding of Sylow subgroups. Sib. Math. J., 2016, vol. 57, no. 2, pp. 200–212.
13. Murashka V. I. Classes of finite groups with generalized subnormal cyclic primary subgroups. Sib. Math. J., 2014, vol. 55, no. 6, pp. 1105–1115.
14. Murashka V. I. Finite groups with given sets of F-subnormal subgroups. Asian-European J. Math., 2020, vol. 13, no. 1, art. 2050073 (13 p.)
15. Carter R., Fischer B., Hawkes T. Extreme classes of finite soluble groups. J. Algebra, 1969, vol. 9, pp. 285–313.
16. Semenchuk V. N. Minimal non-F-groups. Algebra Logika, 1979, vol. 18, no. 3, pp. 348–382 (in Russian).
17. Vasil’ev A. F. A problem in the theory of formations of finite groups. Math. Notes, 1997, vol. 62, no. 1, pp. 44–49.
18. Balychev S. V., Vegera A. S. Soluble saturated formations with the P2 property for finite groups. Probl. Fiz. Mat. Tekh., 2020, no. 1(42), pp. 74–80 (in Russian).
19. Doerk K., Hawkes T. Finite soluble groups. Berlin, New York, Walter de Gruyter, 1992. 891 p.
20. Vasil’ev A. F., Vasilyeva T. I. On finite groups whose principal factors are simple groups. Russian Math. (Iz. VUZ), 1997, vol. 41, no. 11, pp. 8–12.
Review
For citations:
Murashka V.I. On the classes of finite groups defined by the systems of generalized subnormal subgroups. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2024;32(1):25-30. (In Russ.)
Views: 121
Email this article 