On lattices of generalized subnormal subgroups in finite metanilpotent groups
Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 48-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Shemetkov problem about description of hereditary saturated lattice formations and lattice subgroup functors in the class of all finite metanilpotent groups has been solved.
Keywords: finite group, lattice formation, lattice subgroup functor, $\mathfrak{F}$-subnormal subgroup.
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A. F. Vasil'ev; I. N. Khalimonchik. On lattices of generalized subnormal subgroups in finite metanilpotent groups. Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 48-52. http://geodesic.mathdoc.fr/item/PFMT_2015_2_a6/

[1] H. Wielandt, “Eine Verallgemeinerung der invarianten Untergruppen”, Math. Z., 45 (1939), 209–244 | MR

[2] T. Hawkes, “On formations subgroups of a finite soluble groups”, J. London Math. Soc., 44 (1969), 243–250 | MR | Zbl

[3] L. A. Shemetkov, Formations of finite groups, Nauka, M., 1978 | MR | Zbl

[4] A. Ballester-Bolinches, K. Doerk, M. D. Perez-Ramos, “On the lattice on $\mathfrak{F}$-subnormal subgroups”, J. Algebra, 115 (1992), 393–396 | MR

[5] A. F. Vasil'ev, S. F. Kamornikov, V. N. Semenchuk, “On lattices of subgroups of finite groups”, Infinite groups and related algebraic structures, ed. N. S. Chernikov, Institut Matematiki AN Ukrainy, Kiev, 1993, 27–54 | MR | Zbl

[6] A. F. Vasil'ev, S. F. Kamornikov, “On Kegel–Shemetkov problem on lattices of generalized subnormal subgroups of finite groups”, Algebra Logika, 41:4 (2002), 411–428 | MR | Zbl

[7] I. N. Khalimonchik, A. F. Vasil'ev, “On lattices of subgroups subnormal type in finite groups”, Proceedings of the Institute of Mathematics, 21:1 (2013), 25–34

[8] I. N. Khalimonchik, A. F. Vasil'ev, “Conditionally lattice formations of finite groups”, Proceedings of the F. Scorina Gomel State University, 47:2 (2008), 50–55

[9] A. F. Vasil'ev, S. F. Kamornikov, “On the functor method for studing of lattices of subgroups of finite groups”, Sibirsk. Math. Zh., 2 (2001), 30–40 | MR

[10] S. F. Kamornikov, “On a class of lattice subgroup functors”, Mathematical Notes, 89:3–4 (2011), 340–348 | MR | Zbl

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

[12] K. Doerk, T. Hawkes, Finite soluble groups, Walter de Gruyter, Berlin–New York, 1992 | MR

[13] S. F. Kamornikov, M. V. Selkin, Subgroup functors and classes of finite groups, Belaruskaya nauka, Minsk, 2003

[14] I. N. Khalimonchik, “Shemetkov formation in class $\mathfrak{X}$”, Proceedings of the F. Scorina Gomel State University, 55:4 (2009), 219–223 | Zbl