On Lockett conjecture for $\sigma$-local Fitting classes
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2022), pp. 14-20.

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In this paper we find families of generalized local Fitting classes for which the Lockett conjecture is true. It is proved that each generalized local Fitting class is defined as the intersection of the Lockett class and some normal Fitting class.
Keywords: Fiting class, $\sigma$-local Fitting class, Lockett conjecture.
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N. T. Vorob'ev; E. D. Volkova. On Lockett conjecture for $\sigma$-local Fitting classes. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2022), pp. 14-20. http://geodesic.mathdoc.fr/item/IVM_2022_11_a1/

[1] Doerk K., Hawkes T., Finite Soluble Groups, Walter de Gruyter Co., Berlin–New York, 1992 | MR

[2] Lockett F. P., “The Fitting class $\mathfrak{F}^{\ast}$”, Math. Z., 137:2 (1974), 131–136 | DOI | MR

[3] Bryce R. A., Cossey J., “A problem in the Theory of Normal Fitting Classes”, Math. Z., 141:2 (1975), 99–110 | DOI | MR

[4] Beidleman J. C., Hauck P., “Über Fittingklassen und die Lockett-Vermuntung”, Math. Z., 167:2 (1979), 161–167 | DOI | MR

[5] Vorobev N. T., “O radikalnykh klassakh konechnykh grupp s usloviem Loketta”, Matem. zametki, 43:2 (1988), 161–168 | MR

[6] Gallego M. P., “Fitting pairs from direct limits and the Lockett conjecture”, Comm. Algebra, 24:6 (1996), 2011–2023 | DOI | MR

[7] Pense J., “Fittingmengen und Lockettabschnitte”, J. Algebra, 133:1 (1990), 168–181 | DOI | MR

[8] Skiba A. N., “On one generalization of the local formations”, PFMT, 2018, no. 1(34), 79–82 | MR

[9] Skiba A. N., “A generalization of a Hall theorem”, J. Algebra and Appl., 15:5 (2016), 21–36 | DOI | MR

[10] Skiba A. N., “Some characterizations of finite $\sigma$-soluble $P\sigma T$-groups”, J. Algebra, 495:1 (2018), 114–129 | DOI | MR

[11] Skiba A. N., “On sublattices of the subgroup lattice defined by formation Fitting sets”, J. Algebra, 550:5 (2020), 69–85 | DOI | MR

[12] Guo W., Zhang L., Vorob'ev N.T., “On $\sigma$-local Fitting classess”, J. Algebra, 542:15 (2020), 116–129 | DOI | MR

[13] Guo W., Shum K. P., Vorob'ev N.T., “Problems related to the Lockett Conjecture on Fitting classes of finite groups”, Indag. Math. (NS), 19:3 (2008), 391–399 | DOI | MR

[14] Laue H., “Über nichtauflösbare normale Fittingklassen”, J. Algebra, 45:2 (1977), 274–283 | DOI | MR

[15] Berger T. R., “Normal Fitting pairs and Lockett's conjecture”, Math. Z., 163:2 (1978), 125–132 | DOI | MR

[16] Nereshennye voprosy teorii grupp. Kourovskaya tetrad, 18-e izd., dopoln., Izd-vo In-ta matem. SO RAN, Novosibirsk, 2014

[17] Berger T. R., Cossey J., “An Example in the theory of Normal Fitting classes”, Math. Z., 154:3 (1977), 287–293 | DOI | MR

[18] Guo W., Structure Theory for Canonical Classes of Finite Groups, Springer–Verlag, Berlin-Heidelberg, 2015 | MR