Abstract
In the article we study \(\omega\)-fibered and \(\Omega\)-foliated formations and Fitting classes of finite groups which are constructed using two functions named a function-satellite and a function-direction. We have established some properties of functions-directions which give new examples of \(\omega\)-fibered and \(\Omega\)-foliated formations and Fitting classes of finite groups.
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REFERENCES
W. Gaschutz, ‘‘Zur Theorie der endlichen auflosbaren Gruppen,’’ Math. Z. 80, 300–305 (1963).
L. A. Shemetkov, ‘‘Stepped formations of groups,’’ Math. Sb. 94, 628–648 (1974).
B. Hartley, ‘‘On Fischer’s dualization of formation theory,’’ Proc. London Math. Soc. 3 (9), 193–207 (1969).
L. A. Shemetkov, Formations of Finite Groups (Nauka, Moscow, 1978) [in Russian].
L. A. Shemetkov and A. N. Skiba, Formations of Algebraic Systems (Nauka, Moscow, 1989) [in Russian].
A. N. Skiba, Algebra of Formations (Belarus. Nauka, Minsk, 1997) [in Russian].
K. Doerk and T. Hawkes, Finite Soluble Groups (Walter de Gruyter, Berlin, New Jork, 1992).
A. N. Skiba and L. A. Shemetkov, ‘‘Multiply \(\omega\)-local formations and Fitting classes of finite groups,’’ Sib. Adv. Math. 10, 112–141 (2000).
A. N. Skiba and L. A. Shemetkov, ‘‘Multiply \(\mathfrak{L}\)-composition formations of finite groups,’’ Ukr. Math. J. 52, 783–797 (2000).
N. N. Vorobyov, Algebra of Classes of Finite Groups (Belorus. Gos. Univ. im. P. M. Masherova, Vitebsk, 2012) [in Russian].
V. A. Vedernikov and M. M. Sorokina, ‘‘\(\omega\)-fibered formations and fitting classes of finite groups,’’ Math. Notes 71, 39–55 (2002).
V. A. Vedernikov and M. M. Sorokina, ‘‘\(\Omega\)-foliated formations and fitting classes of finite groups,’’ Discrete Math. Appl. 11, 507–527 (2001).
V. A. Vedernikov, ‘‘Maximal satellites of \(\Omega\)-foliated formations and fitting classes,’’ Proc. Steklov Inst. Math. 7 (2), 55–71 (2001).
V. A. Vedernikov, ‘‘On new types of \(\omega\)-fibered formations of finite groups,’’ in Proceedings of the Ukrainian Mathematical Congress – 2001, Section 1: Algebra and Number Theory, Kiev, 2001 (2002), pp. 36–45.
V. A. Vedernikov, ‘‘On new types of \(\omega\)-fibered Fitting classes of finite groups,’’ Ukr. Math. J. 54, 897–903 (2002).
Yu. A. Elovikova, ‘‘Properties of the lattice of all multiply \(\Omega\)-canonical formations,’’ Discrete Math. Appl. 16, 307–317 (2006).
O. V. Kamozina, ‘‘Non-singly-generated multiply \(\omega\)-fan Fitting classes of finite groups,’’ Math. Notes 79, 366–376 (2006).
V. E. Egorova, ‘‘Critical non-singly-generated totally canonical fitting classes of finite groups,’’ Math. Notes 83, 478–484 (2008).
A. B. Elovikov, ‘‘The factorisation of one-generated partially foliated formations,’’ Discrete Math. Appl. 19, 411–430 (2009).
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Sorokina, M.M., Maksakov, S.P. On the Directions of \(\boldsymbol{\omega}\)-Fibered and \(\boldsymbol{\Omega}\)-Foliated Formations and Fitting Classes of Finite Groups. Lobachevskii J Math 41, 273–279 (2020). https://doi.org/10.1134/S199508022002016X
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DOI: https://doi.org/10.1134/S199508022002016X