Geodesic
On the intersection of all maximal $\mathfrak F$-subgroups of a finite group
Problemy fiziki, matematiki i tehniki, no. 3 (2010), pp. 56-62.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mathfrak F$ be a class of groups. A subgroup $H$ of a group $G$ is said to be a maximal $\mathfrak F$-subgroup of $G$ if $H \in \mathfrak F$ and has no a subgroup $E \in \mathfrak F$ such that $H \le E$. The symbol $\Sigma_{\mathfrak F}(G)$ denotes the intersection of all maximal $\mathfrak F$-subgroups of $G$. We study the influence of the subgroup $\Sigma_{\mathfrak F}(G)$ on the structure of $G$.
Keywords: saturated formation, hereditary formation, minimal subgroup, maximal $\mathfrak F$-subgroup, $\mathfrak F$-hypercentre, supersoluble group, $S$-quasinormal subgroup.
Mots-clés : soluble group 
@article{PFMT_2010_3_a8,
     author = {A. N. Skiba},
     title = {On the intersection of all maximal $\mathfrak F$-subgroups of a finite group},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {56--62},
     publisher = {mathdoc},
     number = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2010_3_a8/}
}
TY  - JOUR
AU  - A. N. Skiba
TI  - On the intersection of all maximal $\mathfrak F$-subgroups of a finite group
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2010
SP  - 56
EP  - 62
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2010_3_a8/
LA  - en
ID  - PFMT_2010_3_a8
ER  - 
%0 Journal Article
%A A. N. Skiba
%T On the intersection of all maximal $\mathfrak F$-subgroups of a finite group
%J Problemy fiziki, matematiki i tehniki
%D 2010
%P 56-62
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2010_3_a8/
%G en
%F PFMT_2010_3_a8
A. N. Skiba. On the intersection of all maximal $\mathfrak F$-subgroups of a finite group. Problemy fiziki, matematiki i tehniki, no. 3 (2010), pp. 56-62. http://geodesic.mathdoc.fr/item/PFMT_2010_3_a8/

[1] R. Laue, “Dualization for saturation for locally defined formations”, J. Algebra, 52 (1978), 347–353 | DOI | MR | Zbl

[2] H. G. Bray et al., Between Nilpotent and Solvable, ed. M. Weinstein, Polugonal Publishing House, 1982 | MR | Zbl

[3] Huppert B., Endliche Gruppen, v. I, Springer-Verlag, Berlin–Heidelberg–New York, 1967 | MR | Zbl

[4] J. Buckley, “Finite groups whose minimal subgroups are normal”, Math. Z., 15 (1970), 15–17 | DOI | MR | Zbl

[5] A. Ballester-Bolinches, X. Y. Guo, “On complemented subgroups of finite groups”, Arch. Math., 72 (1999), 161–166 | DOI | MR | Zbl

[6] A. Shaalan, “The influence of $\pi$-quasinormality of some subgroups on the structure of a finite group”, Acta Math. Hungar., 56 (1990), 287–293 | DOI | MR | Zbl

[7] R. K. Agrawal, “Generalized center and hypercenter of a finite group”, Proc. Amer. Math. Soc., 54 (1976), 13–21 | DOI | MR

[8] H. Wielandt, “Uber die Normalstrukture von mehrfach faktorisierbaren Gruppen”, B. Austral. Math. Soc., 1 (1960), 143–146 | DOI | MR | Zbl

[9] O. H. Kegel, “Zur Struktur mehrafach faktorisierbarer endlicher Gruppen”, Math. Z., 87 (1965), 409–434 | DOI | MR

[10] O. Kegel, “Sylow-Gruppen and Subnormalteiler endlicher Gruppen”, Math. Z., 78 (1962), 205–221 | DOI | MR | Zbl

[11] H. Wielandt, Subnormal subgroups and permutation groups, Lectures given at the Ohio State University, Columbus, Ohio, 1971

[12] L. A. Shemetkov, A. N. Skiba, Formations of algebraic systems, Nauka, M., 1989 | MR

[13] Wenbin Guo, The Theory of Classes of Groups, Science Press-Kluwer Academic Publishers, Beijing–New York–Dordrecht–Boston–London, 2000 | MR

[14] K. Doerk, T. Hawkes, Finite Soluble Groups, Walter de Gruyter, Berlin–New York, 1992 | MR

[15] L. A. Shemetkov, A. N. Skiba, “$\omega$-local Formations and Fitting classes of finite groups”, Advances of Math. Siberian, 10:2 (2000), 112–141 | MR | Zbl

[16] L. A. Shemetkov, Formations of Finite Groups, Nauka, M., 1978 | MR | Zbl

[17] D. Gorenstein, Finite Groups, Harper Row Publishers, New York–Evanston–London, 1968 | MR | Zbl

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