Geodesic
On a Class of Groups with Given Cofactors of Maximal Subgroups
Matematičeskie zametki, Tome 87 (2010) no. 5, pp. 643-649 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is devoted to the solution of the general problem of describing finite solvable groups all of whose cofactors of maximal subgroups belong to a given class $\mathfrak X$ of groups. The cases in which $\mathfrak X$ is a homomorph, a Schunk class, and a formation are treated separately. The approach suggested here is related to the construction of a local Schunk class defined by using a constant group function.
Keywords: maximal subgroup, cofactor, Schunk class, primitive group, non-Frattini chief factor.
Mots-clés : finite solvable group, homomorph, formation 
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L. P. Avdashkova; S. F. Kamornikov. On a Class of Groups with Given Cofactors of Maximal Subgroups. Matematičeskie zametki, Tome 87 (2010) no. 5, pp. 643-649. http://geodesic.mathdoc.fr/item/MZM_2010_87_5_a0/

[1] K. Doerk, T. Hawkes, Finite Soluble Groups, de Gruyter Exp. Math., 4, Walter de Gruyter, Berlin, 1992 | MR | Zbl

[2] Ya. G. Berkovich, “Konechnye gruppy s bolshimi yadrami maksimalnykh podgrupp”, Sib. matem. zhurn., 9:2 (1968), 243–248 | MR | Zbl

[3] S. M. Evtukhova, V. S. Monakhov, “Konechnye gruppy s poryadkami kofaktorov podgrupp, svobodnymi ot kvadratov”, Dokl. NAN Belarusi, 49:2 (2005), 26–29 | MR | Zbl

[4] S. M. Evtukhova, V. S. Monakhov, “Konechnye gruppy s $\mathfrak H$-kofaktorami maksimalnykh podgrupp”, Kh Belorusskaya matematicheskaya konferentsiya, Tezisy dokladov, Faktorial, Minsk, 2008, 24–25

[5] R. Baer, “Classes of finite groups and their properties”, Illinois J. Math., 1 (1957), 115–187 | MR | Zbl

[6] L. A. Shemetkov, Formatsii konechnykh grupp, Sovremennaya algebra, Nauka, M., 1978 | MR | Zbl

[7] H. Schunck, “$\mathfrak H$-Untergruppen in endlichen auflösbaren Gruppen”, Math. Z., 97 (1967), 326–330 | DOI | MR | Zbl