Geodesic
Intersections of maximal subgroups in a finite group in connection with the local formations and a generally abnormally full subgroup $m$-functor
Problemy fiziki, matematiki i tehniki, no. 2 (2017), pp. 31-39 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $\pi$ be a set of primes. The sufficient conditions that must satisfy a local formation $\mathfrak{F}=\mathfrak{G}_{\pi}\mathfrak{F}$, a finite group $G$ and a subgroup $m$-functor $\theta$, under which $\overline{\Delta}_{\pi}^{\mathfrak{F}}(G)=\Phi_{\theta_{\pi}}^{\mathfrak{F}}(G)=\Delta_{\pi}^{\mathfrak{F}}(G)\in\mathfrak{F}$ also $\overline{\Delta}_{\pi,\overline{G_{\mathfrak{F}}}}^{\mathfrak{F}}(G)=\Phi_{\theta_{\pi},\overline{G_{\mathfrak{F}}}}^{\mathfrak{F}}(G)=\Phi_{\theta_{\pi}}^{\mathfrak{F}}(G)=\Delta_{\pi}^{\mathfrak{F}}(G)\subset G_{\mathfrak{F}}\subset G$, if $\mathfrak{F}=\mathfrak{G}_{\pi}\mathfrak{F}$ is radical, are achieved. As the consequences of the main results there were obtained the assertions for $\pi=\varnothing$ and corresponding local formations.
Keywords: maximal subgroups of finite groups, local and local radical formations, subgroup $m$-functor. 
@article{PFMT_2017_2_a5,
     author = {L. M. Belokon},
     title = {Intersections of maximal subgroups in a finite group in connection with the local formations and a generally abnormally full subgroup $m$-functor},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {31--39},
     year = {2017},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2017_2_a5/}
}
TY  - JOUR
AU  - L. M. Belokon
TI  - Intersections of maximal subgroups in a finite group in connection with the local formations and a generally abnormally full subgroup $m$-functor
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2017
SP  - 31
EP  - 39
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/PFMT_2017_2_a5/
LA  - ru
ID  - PFMT_2017_2_a5
ER  - 
%0 Journal Article
%A L. M. Belokon
%T Intersections of maximal subgroups in a finite group in connection with the local formations and a generally abnormally full subgroup $m$-functor
%J Problemy fiziki, matematiki i tehniki
%D 2017
%P 31-39
%N 2
%U http://geodesic.mathdoc.fr/item/PFMT_2017_2_a5/
%G ru
%F PFMT_2017_2_a5
L. M. Belokon. Intersections of maximal subgroups in a finite group in connection with the local formations and a generally abnormally full subgroup $m$-functor. Problemy fiziki, matematiki i tehniki, no. 2 (2017), pp. 31-39. http://geodesic.mathdoc.fr/item/PFMT_2017_2_a5/

[1] L.A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978, 272 pp.

[2] L.M. Belokon, “O peresecheniyakh maksimalnykh podgrupp konechnykh grupp”, Problemy fiziki, matematiki i tekhniki, 2014, no. 4(21), 46–59

[3] S.F. Kamornikov, M.V. Selkin, Podgruppovye funktory i klassy konechnykh grupp, Bel. navuka, Mn., 2003, 254 pp.

[4] M.V. Selkin, R.V. Borodich, “O peresecheniyakh maksimalnykh podgrupp konechnykh grupp”, Vestnik SamGU–Estestvennonauchnaya seriya, 2009, no. 8(74), 67–76

[5] E.N. Borodich, R.V. Borodich, “O peresecheniyakh $\mathfrak{F}$-abnormalnykh maksimalnykh $\theta$-podgrupp”, Vestsi Natsyyanalnai Akademii Navuk Belarusi, 2007, no. 3, 47–52

[6] L.M. Belokon, “K voprosu o peresecheniyakh maksimalnykh $\theta$-podgrupp konechnykh grupp”, Problemy fiziki, matematiki i tekhniki, 2015, no. 3(24), 46–50

[7] L.M. Belokon, “O peresecheniyakh maksimalnykh $\theta_\pi$-podgrupp konechnykh grupp i $\mathfrak{F}$-abnormalno $\pi'$-polnyi podgruppovoi $m$-funktor”, Problemy fiziki, matematiki i tekhniki, 2015, no. 4(25), 50–58

[8] L.M. Belokon, “Peresecheniya maksimalnykh podgrupp konechnykh grupp i radikalnye formatsii”, Izvestiya Gomelskogo gosudarstvennogo universiteta im. F. Skoriny, 2013, no. 6(81), 3–10

[9] L.M. Belokon, “Normalnaya faktorizuemost subnormalnoi v konechnoi gruppe podgruppy v svyazi s lokalnymi formatsiyami i obobschennymi podgruppami Frattini. Formatsionnye radikaly”, Problemy fiziki, matematiki i tekhniki, 2017, no. 1(30), 26–36

[10] R.V. Borodich, M.V. Selkin, “O nekotorykh svoistvakh $\mathfrak{F}$-abnormalnykh podgrupp konechnykh grupp”, Izvestiya Gomelskogo gosudarstvennogo universiteta im. F. Skoriny, 2010, no. 3(60), 197–201

[11] M.V. Selkin, V.N. Semenchuk, “Peresechenie maksimalnykh podgrupp v konechnykh gruppakh”, Voprosy algebry, 1985, no. 1, 67–72