V. A. Vedernikov, M. M. Sorokina, “$\omega$-Fibered Formations and Fitting Classes of Finite Groups”, Mat. Zametki, 71:1 (2002), 43–60; Math. Notes, 71:1 (2002), 39

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Matematicheskie Zametki, 2002, Volume 71, Issue 1, Pages 43–60
DOI: https://doi.org/10.4213/mzm327 (Mi mzm327)

This article is cited in 23 scientific papers (total in 23 papers)

$\omega$ -Fibered Formations and Fitting Classes of Finite Groups

V. A. Vedernikov^a, M. M. Sorokina^b

^a Moscow City Pedagogical University
^b I. G. Petrovsky Bryansk State Pedagogical University

Full-text PDF (254 kB) Citations (23)

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DOI: https://doi.org/10.4213/mzm327

Abstract: In this paper, we suggest a new functional approach to the study of group classes which enables us to describe all formations and Fitting classes of finite groups in the language of functions. The notions of

$\omega$ -fibered formation and of

$\omega$ -fibered Fitting class with direction

$\varphi$ are introduced. A direction

$\varphi$ is defined as a mapping of the set

$\mathbb P$ of all primes into the set of all nonempty Fitting formations. The existence of infinitely many mappings of this kind makes it possible to construct new forms of formations and Fitting classes for a given nonempty set

$\omega$ . In particular, an

$\omega$ -local formation is an

$\omega$ -fibered formation with a direction

$\varphi$ such that

$\varphi (p)=\mathfrak G_{p'}\mathfrak N_p$ for any prime

$p$ . In the paper we study some basic properties of

$\omega$ -fibered formations and of

$\omega$ -fibered Fitting classes with direction

$\varphi$ and obtain the structure of their minimal satellites for a given

$\varphi$ .

Received: 20.07.2000

English version:
Mathematical Notes, 2002, Volume 71, Issue 1, Pages 39–55
DOI: https://doi.org/10.1023/A:1013922206539

Bibliographic databases:

UDC: 512.542

Language: Russian

Citation: V. A. Vedernikov, M. M. Sorokina, “

$\omega$ -Fibered Formations and Fitting Classes of Finite Groups”, Mat. Zametki, 71:1 (2002), 43–60; Math. Notes, 71:1 (2002), 39–55

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm327

https://doi.org/10.4213/mzm327

https://www.mathnet.ru/eng/mzm/v71/i1/p43

This publication is cited in the following 23 articles:

M. M. Sorokina, A. S. Nesterov, “O sputnikakh $\sigma_\Omega$ -rassloennykh formatsii grupp”, Diskret. matem., 36:1 (2024), 103–115
S. P. Maksakov, M. M. Sorokina, “O brauerovykh reshetkakh $\omega$ -veernykh formatsii konechnykh grupp”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2024, no. 3, 5–17
M. M. Sorokina, D. G. Novikova, “O $\frak F^{\omega}$ -proektorakh i $\frak F^{\omega}$ -pokryvayuschikh podgruppakh konechnykh grupp”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 24:4 (2024), 526–535
S. P. Maksakov, M. M. Sorokina, “On algebraicity of lattices of $\omega$ -fibred formations of finite groups”, Discrete Math. Appl., 33:5 (2023), 283–291
A. A. Gorepekina, M. M. Sorokina, “ $\bar\omega$ -sputniki $\bar\omega$ -veernykh formatsii konechnykh grupp”, Tr. IMM UrO RAN, 28, no. 2, 2022, 106–113
S. P. Maksakov, “On the lattices of the $\omega$ -fibered formations of finite groups”, Tr. IMM UrO RAN, 27, no. 1, 2021, 258–267
N. N. Vorob'ev, I. I. Stasel'ko, A. O. Hojagulyyev, “Separated lattices of multiply $\sigma$ -local formations”, Siberian Math. J., 62:4 (2021), 586–597
M. M. Sorokina, A. A. Gorepekina, “ $\bar \omega$ -veernye formatsii konechnykh grupp”, Chebyshevskii sb., 22:3 (2021), 232–244
M. M. Sorokina, S. P. Maksakov, “On the Normality of $\mathfrak F^{\omega}$ -Abnormal Maximal Subgroups of Finite Groups”, Math. Notes, 108:3 (2020), 409–418
Sorokina M.M. Maksakov S.P., “On the Directions of Omega-Fibered and Omega-Foliated Formations and Fitting Classes of Finite Groups”, Lobachevskii J. Math., 41:2, SI (2020), 273–279
O. V. Kamozina, “ $\omega\sigma$ -veernye klassy Fittinga”, Chebyshevskii sb., 21:4 (2020), 107–116
Yang N., Li B., Vorob'ev N.T., “On the Dual Theory of a Result of Bryce and Cossey”, J. Algebra, 522 (2019), 124–133
E. N. Bazhanova, V. A. Vedernikov, “ $\Omega$ -rassloennye klassy Fittinga $T$ -grupp”, Sib. elektron. matem. izv., 14 (2017), 629–639
V. A. Vedernikov, M. M. Sorokina, “The $\mathfrak F^\omega$ -normalizers of finite groups”, Siberian Math. J., 58:1 (2017), 49–62
V. A. Vedernikov, M. M. Sorokina, “On complements of coradicals of finite groups”, Sb. Math., 207:6 (2016), 792–815
V. A. Vedernikov, M. M. Sorokina, “ $\mathfrak F$ -projectors and $\mathfrak F$ -covering subgroups of finite groups”, Siberian Math. J., 57:6 (2016), 957–968
M. A. Korpacheva, M. M. Sorokina, “The critical $\omega$ -foliated $\tau$ -closed formations of finite groups”, Discrete Math. Appl., 21:1 (2011), 69–77
V. A. Vedernikov, E. N. Demina, “ $\Omega$ -foliated formations of multioperator $T$ -groups”, Siberian Math. J., 51:5 (2010), 789–804
E. N. Zalesskaya, N. N. Vorob'ev, “Lattices of partially local fitting classes”, Siberian Math. J., 50:6 (2009), 1038–1044
V. M. Selkin, “O minimalnykh $\tau$ -zamknutykh $\omega$ -lokalnykh ne $\mathfrak H$ -formatsiyakh”, Tr. In-ta matem., 16:1 (2008), 81–85

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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