On the classes of finite groups defined by the systems of generalized subnormal subgroups

V. I. Murashka

Trudy Instituta matematiki, Tome 32 (2024) no. 1, pp. 25-30.

Résumé

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.

Détail

Keywords: finite group, $\mathfrak{F}$-subnormal subgroup, saturated formation, Fitting formation.

Bibliographie

[1] Vasil’ev A. F, Vasil’eva T. I., Tyutyanov V. N., “On the finite groups of supersoluble type”, Sib. Math. J., 51:6 (2010), 1004–1012 | DOI | MR | Zbl

[2] Monakhov V. S., Kniahina V. N., “Finite groups with $\mathbb{P}$-subnormal subgroups”, Ricerche mat., 62 (2013), 307–322 | DOI | MR | Zbl

[3] Hawkes T. O., “On formation subgroups of a finite soluble group ”, J. London Math. Soc., 4 (1969), 243–250 | DOI | MR

[4] Shemetkov L. A., Formations of finite groups, Nauka, M., 1978, 272 pp. (in Russian)

[5] Kamornikov S. F., Selkin M. V., Subgroups functors and classes of finite groups, Belaruskaya nauka, Minsk, 2003, 254 pp. (in Russian)

[6] Ballester-Bollinches A., Ezquerro L. M., Classes of Finite Groups, Math. Appl., 584, Springer, Netherlands, 2006, 385 pp. | MR

[7] Vasil'ev A. F., Vasilyeva T. I., “On finite groups with generally subnormal Sylow subgroups”, Probl. Fiz. Mat. Tekh., 2011, no. 4(9), 86–91 (in Russian) | Zbl

[8] Semenchuk V. N. Shevchuk S. N., “Characterization of classes of finite groups with the use of generalized subnormal Sylow subgroups”, Math. Notes, 89:1 (2011), 117–120 | DOI | DOI | MR | Zbl

[9] Vasil’eva T. I., Koranchuk A. G., “Finite Groups with Subnormal Residuals of Sylow Normalizers”, Sib. Math. J., 63:4 (2022), 670–676 | DOI | MR

[10] Monakhov V. S., Sokhor I. L., “On groups with formational subnormal Sylow subgroups ”, J. Group Theory, 21 (2018), 273–287 | DOI | MR | Zbl

[11] Guo W., Skiba A. N., “Finite groups whose $n$-maximal subgroups are $\sigma$-subnormal”, Sci. China Math., 62:7 (2019), 1355–1372 | DOI | MR | Zbl

[12] Vasil’ev A. F., Vasil’eva T. I., Vegera A. S., “Finite groups with generalized subnormal embedding of Sylow subgroups”, Sib. Math. J., 57:2 (2016), 200–212 | DOI | MR | Zbl

[13] Murashka V. I., “Classes of finite groups with generalized subnormal cyclic primary subgroups”, Sib. Math. J., 55:6 (2014), 1105–1115 | DOI | MR | Zbl

[14] Murashka V. I., “Finite groups with given sets of F-subnormal subgroups”, Asian-European J. Math., 13:1 (2020), 2050073, 13 pp. | DOI | MR | Zbl

[15] Carter R., Fischer B., Hawkes T., “Extreme classes of finite soluble groups”, J . Algebra, 9 (1969), 285–313 | DOI | MR

[16] Semenchuk V. N., “Minimal non-$\mathfrak{F}$-groups”, Algebra Logika, 18:3 (1979), 348–382 (in Russian) | Zbl

[17] Vasil'ev A. F., “A problem in the theory of formations of finite groups”, Math. Notes, 62:1 (1997), 44–49 | DOI | DOI | MR | Zbl

[18] Balychev S. V., Vegera A. S., “Soluble saturated formations with the $\mathcal{P}_2$ property for finite groups”, Probl. Fiz. Mat. Tekh., 2020, no. 1(42), 74–80 (in Russian) | Zbl

[19] Doerk K., Hawkes T., Finite soluble groups, Walter de Gruyter, Berlin–New York, 1992, 891 pp. | MR

[20] Vasil'ev A. F., Vasilyeva T. I., “On finite groups whose principal factors are simple groups”, Russian Math. (Iz. VUZ), 41:11 (1997), 8–12 | MR | Zbl