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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.

About the Author

V. I. Murashka
Francisk Skoryna Gomel State University
Belarus

Gomel



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.


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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.)

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ISSN 1812-5093 (Print)