Geodesic
About the intersection of the maximal subgroups of finite groups
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 67-77 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The structure of normal subgroups in $\Theta $-frattini expansions is established in the given work. Local Fitting $\frak F$ formation contains all nilpotent groups. For this formations we show that in solvable group the intersection $\frak F$-abnormal maximal $\Theta$-subgroups, which don't contain $\frak F$-radical and don't belong to $\frak F$, coincides with the intersection $\frak F$-abnormal maximal $\Theta $-subgroups and belongs formation $\frak F$.
Mots-clés : group, local formation
Keywords: Fitting formation, $m$-functor, abnormal maximal subgroup. 
@article{VSGU_2009_8_a6,
     author = {M. V. Sel'kin and R. V. Borodich},
     title = {About the intersection of the maximal subgroups of finite groups},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {67--77},
     year = {2009},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2009_8_a6/}
}
TY  - JOUR
AU  - M. V. Sel'kin
AU  - R. V. Borodich
TI  - About the intersection of the maximal subgroups of finite groups
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2009
SP  - 67
EP  - 77
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/VSGU_2009_8_a6/
LA  - ru
ID  - VSGU_2009_8_a6
ER  - 
%0 Journal Article
%A M. V. Sel'kin
%A R. V. Borodich
%T About the intersection of the maximal subgroups of finite groups
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2009
%P 67-77
%N 8
%U http://geodesic.mathdoc.fr/item/VSGU_2009_8_a6/
%G ru
%F VSGU_2009_8_a6
M. V. Sel'kin; R. V. Borodich. About the intersection of the maximal subgroups of finite groups. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 67-77. http://geodesic.mathdoc.fr/item/VSGU_2009_8_a6/

[1] Frattini G., “Intorno alla generasione dei gruppi di operazioni”, Atti Acad. dei Lincei, 1 (1885), 281–285

[2] Gaschütz W., “Über die $\Phi$-Untergruppen endlicher Gruppen”, Math. Z., 1953, no. 58, 160–170 | DOI | MR | Zbl

[3] Deskins W. E., “A condition for the solvability of a finite group”, Ill. J. Math., 5:2 (1961), 306–313 | MR | Zbl

[4] Shidov L. I., “O maksimalnykh podgruppakh konechnykh grupp”, Sib. mat. zh., 12:3 (1971), 682–683 | Zbl

[5] Vedernikov V. A., Duka N. G., “Konechnye gruppy s obobschennoi podgruppoi Frattini”, IX Vsesoyuz. algebraich. kollokvium: materialy, Gomel, 1968, 44

[6] Monakhov V. S., Selkin M. V., “O stroenii normalnykh podgrupp konechnykh grupp”, Voprosy algebry, 1993, 96–100 | MR | Zbl

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

[8] Shemetkov L. A., “Stupenchatye formatsii grupp”, Matem. sb., 94:4 (1974), 628–648 | Zbl

[9] Shlyk V. V., “O peresechenii maksimalnykh podgrupp v konechnykh gruppakh”, Mat. zametki, 14:3 (1973), 429–439

[10] Selkin M. V., Maksimalnye podgruppy v teorii klassov konechnykh grupp, Bel. navuka, Minsk, 1997, 144 pp. | MR

[11] Shemetkov L. A., Skiba A. N., Formatsii algebraicheskikh sistem, Nauka, M., 1989, 253 pp. | MR

[12] Ballester-Bolinches A., Perez-Ramos M. D., “On $\frak F$-subnormal subgroups and Frattini-like subgroups of a finite group”, Glasgow Math. J., 36 (1994), 241–247 | DOI | MR | Zbl

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

[14] Skiba A. N., Algebra formatsii, Bel. navuka, Minsk, 1997, 240 pp. | MR | Zbl

[15] Vasilev A. F., Kamornikov S. F., Semenchuk V. N., “O reshetkakh podgrupp konechnykh grupp”, Beskonechnye gruppy i primykayuschie algebraicheskie sistemy, materialy mezhdunar. algebr. konf., Kiev, 1993, 27–54 | MR

[16] Shemetkov L. A., Formatsii konechnykh grupp, Nauka, M., 1978, 267 pp. | MR | Zbl

[17] Selkin M. V., Sidorov A. V., “Nekotorye obobscheniya podgruppy Frattini”, Voprosy algebry, 1996, no. 9, 138–143 | MR

[18] Borodich R. V., Borodich E. N., “O peresechenii $\frak F$-abnormalnykh maksimalnykh $\Theta$-podgrupp”, Vesti NAN Belarusi. Ser. fiz.-mat. nauk, 2007, no. 3, 47–52 | MR