Geodesic
On the Distributivity and Modularity Properties of the Lattice of Fitting Classes
Matematičeskie zametki, Tome 110 (2021) no. 5, pp. 658-671 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that the lattice of all Fitting classes of finite groups is not distributive, and conditions under which Fitting classes satisfy the distributive and modular laws are determined.
Keywords: Fitting class, $\mathfrak{F}$-radical, lattice of Fitting classes, modular and distributive laws. 
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N. T. Vorob'ev; E. D. Lantsetova. On the Distributivity and Modularity Properties of the Lattice of Fitting Classes. Matematičeskie zametki, Tome 110 (2021) no. 5, pp. 658-671. http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a1/

[1] K. Doerk, T. Hawkes, Finite Soluble Groups, De Gruyter Exp. Math., 4, Walter de Gruyter, Berlin, 1992 | MR

[2] D. Blessenohl, W. Gaschütz, “Über normale Schunk- und Fittingklassen”, Math. Z., 118 (1970), 1–8 | DOI | MR | Zbl

[3] H. Lausch, “On normal Fitting classes”, Math. Z., 130 (1973), 67–72 | DOI | MR | Zbl

[4] N. T. Vorobev, A. V. Martsinkevich, “Konechnye $\pi$-gruppy s normalnymi in'ektorami”, Sib. matem. zhurn., 56:4 (2015), 790–797 | DOI | MR | Zbl

[5] N. N. Vorobev, A. N. Skiba, “O distributivnosti reshetki razreshimykh totalno lokalnykh klassov Fittinga”, Matem. zametki, 67:5 (2000), 662–673 | DOI | MR | Zbl

[6] S. Reifferscheid, On the Theory of Fitting Classes of Finite Soluble Groups, Dissertation, Tübingen, 2001

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

[8] A. N. Skiba, “A generalization of a Hall theorem”, J. Algebra Appl., 15:5 (2015), 1650085 | MR

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

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

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

[12] A. N. Skiba, Algebra formatsii, Belaruskaya navuka, Minsk, 1997 | MR

[13] Kourovskaya tetrad. Nereshennye voprosy teorii grupp, 14-e izd., In-t matem. SO RAN, Novosibirsk, 1999 | MR

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

[15] L. A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978 | MR

[16] E. Cusack, “The join of two Fitting classes”, Math. Z., 167 (1979), 37–47 | DOI | MR | Zbl

[17] N. Yang, Sh. Zhao, A. V. Martsinkevich, N. T. Vorob'ev, “The sublattice of the lattice of $\pi$-normal Fitting classes”, J. Algebra Appl., 19:6 (2020), 2050105 | MR | Zbl

[18] A. V. Martsinkevich, N. T. Vorobev, “Proizvedeniya i ob'edineniya lokalno normalnykh klassov Fittinga”, Tr. IMM UrO RAN, 24, no. 2, 2018, 152–157 | DOI

[19] A. R. Camina, “A Note on Fitting Classes”, Math. Z., 136 (1974), 351–352 | DOI | MR | Zbl

[20] N. T. Vorobev, E. D. Lantsetova, “O reshetochnykh svoistvakh klassov Fittinga”, Vesnik VDU, 98:1 (2017), 5–10

[21] N. T. Vorobev, “O predpolozhenii Khouksa dlya radikalnykh klassov”, Sib. matem. zhurn., 37:6 (1996), 1296–1302 | MR | Zbl