Abstract
Under study is the inclusion regular transitive subgroup functors. We prove that each of these functors is X-subnormal for some class X of primitive groups. We also inspect the structure of a total eigenclass of an inclusion regular transitive functor and the properties of special subgroup lattices.
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Vasil’ev A. F. and Kamornikov S. F., “On the functorial method for studying the lattices of subgroups of finite groups,” Siberian Math. J., 42, No. 1, 25–33 (2001).
Barnes D. W. and Kegel O. H., “Gaschütz functors on finite soluble groups,” Math. Z., Bd 94, Heft 2. S. 134–142 (1966).
Sudbrock W., “Sylowfunktionen in endlichen Gruppen,” Rend. Semin. Mat. Univ. Padova, 36, No. 1, 158–184 (1966).
Mann A., “On subgroups of finite soluble groups. III,” Israel J. Math., 16, No. 4, 446–451 (1973).
Skiba A. N., Algebra of Formations [in Russian], Belarusskaya Nauka, Minsk (1977).
Kamornikov S. F., “On the lattice of regular transitive subgroup functors,” Siberian Math. J., 51, No. 5, 824–829 (2010).
Kamornikov S. F., “On a class of lattice subgroup functors,” Math. Notes, 89, No. 3, 340–348 (2011).
Doerk K. and Hawkes T., Finite Soluble Groups, Walter de Gruyter, Berlin and New York (1992).
Ballester-Bolinches A. and Ezquerro L. M., Classes of Finite Groups, Springer-Verlag, Dordrecht (2006).
Shemetkov L. A., Formations of Finite Groups [in Russian], Nauka, Moscow (1978).
Kamornikov S. F. and Sel’kin V. M., Subgroup Functors and Classes of Finite Groups [in Russian], Belarusskaya Nauka, Minsk (2003).
Gaschütz W., “Zur Theorie der endlichen auflösbaren Gruppen,” Math. Z., 80, No. 4, 300–305 (1963).
Baer R., “Classes of finite groups and their properties,” Illinois J. Math., 1, 115–187 (1957).
Skiba A. N., “On a class of local formations of finite groups” Dokl. Akad. Nauk BSSR, 34, No. 11, 982–985 (1990).
Kamornikov S. F., “On two problems by L. A. Shemetkov,” Siberian Math. J., 35, No. 4, 713–721 (1994).
Semenchuk V. N. and Vasil’ev A. F., “Characterization of local formations F by given properties of minimal non-Fgroups,” in: Studies of Normal and Subgroup Structure of Finite Groups [in Russian], Nauka i Tekhnika, Minsk, 1984, pp. 175–181.
Vasil’ev A. F., Kamornikov S. F., and Semenchuk V. N., “On subgroup lattices of finite groups,” in: Infinite Groups and Related Algebraic Structures [in Russian], Inst. Mat. Akad. Nauk Ukrainy, Kiev, 1993, pp. 27–54.
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Original Russian Text Copyright © 2015 Yi X. and Kamornikov S.F.
Gomel; Hangzhou. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 5, pp. 1057–1067, September–October, 2015; DOI: 10.17377/smzh.2015.56.507.
The first author was supported by the NNSF of China (Grant 11471055).
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Yi, X., Kamornikov, S.F. Inclusion subgroup functors. Sib Math J 56, 844–851 (2015). https://doi.org/10.1134/S0037446615050079
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DOI: https://doi.org/10.1134/S0037446615050079