Geodesic
On complete sublattices of formations of finite groups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2018), pp. 21-26.

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We prove that the lattice of all $\tau$-closed saturated formations of finite groups is a complete sublattice of the lattice of all $\tau$-closed solubly saturated formations of finite groups.
Keywords: finite group, formation of groups, subgroup functor, $\tau$-closed formation, saturated formation, solubly saturated formation, complete lattice of formations, complete sublattice. 
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N. N. Vorob'ev. On complete sublattices of formations of finite groups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2018), pp. 21-26. http://geodesic.mathdoc.fr/item/IVM_2018_1_a2/

[1] Skiba A. N., Algebra formatsii, Belarusk. navuka, Minsk, 1997

[2] Shemetkov L. A., Skiba A. N., Formatsii algebraicheskikh sistem, Sovremen. algebra, Nauka, M., 1989 | MR

[3] Artamonov V. A., Salii V. N., Skornyakov L. A. i dr., Obschaya algebra, v 2 t., v. 2, Sprav. matem. b-ka, ed. L. A. Skornyakov, Nauka, M., 1991

[4] Safonov V. G., Shemetkov L. A., “O podreshetkakh reshetki totalno nasyschennykh formatsii konechnykh grupp”, Dokl. NAN Belarusi, 52:4 (2008), 34–37 | MR | Zbl

[5] Vorobev N. N., Tsarev A. A., “O modulyarnosti reshetki $\tau$-zamknutykh $n$-kratno $\omega$-kompozitsionnykh formatsii”, Ukrainsk. matem. zhurn., 62:4 (2010), 453–463 | MR | Zbl

[6] Skiba A. N., Vorob'ev N.N., “On the lattices of saturated and solubly saturated formations of finite groups”, Southeast Asian Bull. Math., 37:5 (2013), 771–780 | MR | Zbl

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

[8] Doerk K., Hawkes T., Finite Soluble Groups, De Gruyter Expo. Math., 4, Walter de Gruyter Co., Berlin–New York, 1992 | MR

[9] Skiba A. N., “Kharakterizatsiya konechnykh razreshimykh grupp zadannoi nilpotentnoi dliny”, Voprosy algebry, 3, Minsk, 1987, 21–31

[10] Guo Wenbin., The Theory of Classes of Groups, Mathematics and its Applications, 505, Sci. Press/Kluwer Academic Publishers, Beijing–New York–Dordrecht–Boston–London, 2000 | MR | Zbl

[11] Ballester-Bolinches A., Ezquerro L. M., Classes of Finite Groups, Math. and Appl., 584, Springer, Dordrecht, 2006 | MR | Zbl

[12] Vorobev N. N., Algebra klassov konechnykh grupp, Izd-vo VGU imeni P. M. Masherova, Vitebsk, 2012

[13] Skiba A. N., Shemetkov L. A., “Kratno $\omega$-lokalnye formatsii i klassy Fittinga konechnykh grupp”, Matem. tr., 2:2 (1999), 114–147 | MR | Zbl

[14] Skiba A. N., Shemetkov L. A., “Kratno $\mathfrak L$-kompozitsionnye formatsii konechnykh grupp”, Ukrainsk. matem. zhurn., 52:6 (2000), 783–797 | Zbl