Geodesic
The Kegel~-- Shemetkov Problem on Lattices of Generalized Subnormal Subgroups of Finite Groups
Algebra i logika, Tome 41 (2002) no. 4, pp. 411-428.

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

We study into formations $\mathfrak F$ for which the set of all $\mathfrak F$-subnormal ($\mathfrak F$-accessible) subgroups form a sublattice of the lattice of all subgroups in every finite group. A constructive description of all soluble hereditary formations of finite groups with given properties is furnished.
Keywords: finite group
Mots-clés : formation. 
@article{AL_2002_41_4_a1,
     author = {A. F. Vasil'ev and S. F. Kamornikov},
     title = {The {Kegel~--} {Shemetkov} {Problem} on {Lattices} of {Generalized} {Subnormal} {Subgroups} of {Finite} {Groups}},
     journal = {Algebra i logika},
     pages = {411--428},
     publisher = {mathdoc},
     volume = {41},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2002_41_4_a1/}
}
TY  - JOUR
AU  - A. F. Vasil'ev
AU  - S. F. Kamornikov
TI  - The Kegel~-- Shemetkov Problem on Lattices of Generalized Subnormal Subgroups of Finite Groups
JO  - Algebra i logika
PY  - 2002
SP  - 411
EP  - 428
VL  - 41
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2002_41_4_a1/
LA  - ru
ID  - AL_2002_41_4_a1
ER  - 
%0 Journal Article
%A A. F. Vasil'ev
%A S. F. Kamornikov
%T The Kegel~-- Shemetkov Problem on Lattices of Generalized Subnormal Subgroups of Finite Groups
%J Algebra i logika
%D 2002
%P 411-428
%V 41
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2002_41_4_a1/
%G ru
%F AL_2002_41_4_a1
A. F. Vasil'ev; S. F. Kamornikov. The Kegel~-- Shemetkov Problem on Lattices of Generalized Subnormal Subgroups of Finite Groups. Algebra i logika, Tome 41 (2002) no. 4, pp. 411-428. http://geodesic.mathdoc.fr/item/AL_2002_41_4_a1/

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

[2] R. Carter, T. O. Hawkes, “The $\mathfrak F$-normalizers of a finite soluble group”, J. Algebra, 5:2 (1967), 175–202 | DOI | MR | Zbl

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

[4] Nereshennye voprosy teorii grupp. Kourovskaya tetrad, 12-e izd., Novosibirsk, 1992 | MR

[5] O. H. Kegel, “Untergruppenverbände endlicher Gruppen, die Subnormalteilerverband echt enthalten”, Arch. Math., 30:3 (1978), 225–228 | DOI | MR | Zbl

[6] A. F. Vasilev, S. F. Kamornikov, V. N. Semenchuk, “O reshetkakh podgrupp konechnykh grupp”, Beskonechnye gruppy i primykayuschie algebraicheskie sistemy, In-t matem. AN Ukrainy, Kiev, 1993, 27–54 | MR

[7] A. Ballester-Bolinches, K. Doerk, M. D. Perez-Ramos, “On the lattice of $\mathfrak F$-subnormal subgroups”, J. Algebra, 148:2 (1992), 42–52 | DOI | MR | Zbl

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

[9] A. H. Skiba, “Ob odnom klasse lokalnykh formatsii konechnykh grupp”, Dokl. AN BSSR, 34:11 (1990), 382–385 | MR

[10] V. N. Semenchuk, A. F. Vasilev, “Kharakterizatsiya lokalnykh formatsii $\mathfrak F$ po zadannym svoistvam minimalnykh ne $\mathfrak F$-grupp”, Issledovanie normalnogo i podgruppovogo stroeniya konechnykh grupp, Nauka i tekhnika, Minsk, 1984, 175–181 | MR

[11] T. O. Hawkes, “Two applications of twisted wreath products to finite soluble groups”, Trans. Am. Math. Soc., 214:3 (1975), 325–335 | DOI | MR | Zbl