Abstract
We prove that the lattice of all τ-closed saturated formations of finite groups is a complete sublattice of the lattice of all τ-closed solubly saturated formations of finite groups.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Skiba, A. N. Algebra of Formations (Belarusk. Navuka, Minsk, 1997) [in Russian].
Shemetkov, L. A. and Skiba, A. N. “Formations of Algebraic Systems”, in Modern Algebra (Nauka, Moscow, 1989) [in Russian].
Artamonov, V. A. Salii, V. N. Skornyakov, L. A. et al. General Algebra, L. A. Skornyakov (Ed.), Spravochnaya Matematicheskaya Biblioteka (Nauka, Moscow, 1991), Vol. 2 [in Russian].
Safonov, V. G. and Shemetkov, L. A. “Sublattices of the Lattice of Totally Saturated Formations of Finite Groups”, Dokl. Nats. Akad. Belarusi 52, No. 4, 34–37 (2008) [in Russian].
Vorob’ev, N. N. and Tsarev, A. A. “On the Modularity of a Lattice of τ-closed n-Multiply ω-Composite Formations”, Ukr.Mat. Zh. 62, No. 4, 453–463 (2010).
Skiba, A. N. and Vorob’ev, N. N. “On the Lattices of Saturated and Solubly Saturated Formations of Finite Groups”, Southeast Asian Bull.Math. 37, No. 5, 771–780 (2013).
Guo Wenbin, Structure Theory for Canonical Classes of Finite Groups (Springer-Verlag, Berlin–Heidelberg, 2015).
Doerk, K. and Hawkes, T. Finite Soluble Groups, De Gruyter Expo. Math. (Walter de Gruyter & Co., Berlin–New York, 1992), Vol. 4.
Skiba, A. N. “Characterization of Finite Solvable Groups of aGiven Nilpotent Length”, Vopr. Algebry, No. 3, 21–31 (1987) [in Russian].
Guo Wenbin, “The Theory of Classes of Groups”, in Mathematics and its Applications (Sci. Press/Kluwer Academic Publishers, Beijing–New York–Dordrecht–Boston–London, 2000), Vol. 505.
Ballester-Bolinches, A. and Ezquerro, L.M. “Classes of Finite Groups”, in Mathematics and Applications (Springer, Dordrecht, 2006), Vol. 584.
Vorob’ev, N. N. Algebra of Classes of Finite Groups (P. M. Masherov Vitebsk State University, Vitebsk, 2012) [in Russian].
Shemetkov, L. A. and Skiba, A. N. “Multiply ω-Local Formations and Fitting Classes of Finite Groups”, Sib. Adv. Math. 10, No. 2, 112–141 (2000).
Skiba, A. N. and Shemetkov, L. A. “Multiply L-Composite Formations of Finite Groups”, Ukr. Math. J. 52, No. 6, 898–913 (2000).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © N.N. Vorob’ev, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 1, pp. 21–26.
About this article
Cite this article
Vorob’ev, N.N. On Complete Sublattices of Formations of Finite Groups. Russ Math. 62, 17–22 (2018). https://doi.org/10.3103/S1066369X18010036
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X18010036