On the permutability of maximal subgroups with Schmidt subgroups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 126-133
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A Schmidt group is a finite nonnilpotent group in which every proper subgroup is nilpotent. We establish sufficient conditions for the $p$-solvability of a finite group in which maximal subgroups permute with some Schmidt subgroups.
Keywords: finite group, Schmidt subgroup, permutable subgroups.
Mots-clés : solvable group
@article{TIMM_2011_17_4_a13,
     author = {V. N. Knyagina and V. S. Monakhov},
     title = {On the permutability of maximal subgroups with {Schmidt} subgroups},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {126--133},
     year = {2011},
     volume = {17},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a13/}
}
TY  - JOUR
AU  - V. N. Knyagina
AU  - V. S. Monakhov
TI  - On the permutability of maximal subgroups with Schmidt subgroups
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2011
SP  - 126
EP  - 133
VL  - 17
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a13/
LA  - ru
ID  - TIMM_2011_17_4_a13
ER  - 
%0 Journal Article
%A V. N. Knyagina
%A V. S. Monakhov
%T On the permutability of maximal subgroups with Schmidt subgroups
%J Trudy Instituta matematiki i mehaniki
%D 2011
%P 126-133
%V 17
%N 4
%U http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a13/
%G ru
%F TIMM_2011_17_4_a13
V. N. Knyagina; V. S. Monakhov. On the permutability of maximal subgroups with Schmidt subgroups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 126-133. http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a13/

[1] Shmidt O. Yu., “Gruppy, vse podgruppy kotorykh spetsialnye”, Mat. sb., 31:3–4 (1924), 366–372 | Zbl

[2] Monakhov V. S., “Podgruppy Shmidta, ikh suschestvovanie i nekotorye prilozheniya”, Pratsi Ukrain. matem. kongresu-2001, Sekts. 1, In-t matematiki NAN Ukraini, Kiiv, 2002, 81–90 | MR | Zbl

[3] Berkovich Ya. G., Palchik E. M., “O perestanovochnosti podgrupp konechnoi gruppy”, Sib. mat. zhurn., 8:4 (1967), 741–753 | Zbl

[4] Monakhov V. S., Vvedenie v teoriyu konechnykh grupp i ikh klassov, Vysheish. shk., Minsk, 2006, 207 pp.

[5] Huppert B., Endliche Gruppen, v. I, Springer-Verlag, Berlin–Heidelberg–New York, 1967, 793 pp. | MR | Zbl

[6] Monakhov V. S., “O podgruppakh Shmidta konechnykh grupp”, Voprosy algebry, 13, 1998, 153–171

[7] Suzuki M., Group theory, v. II, Springer, New York–Berlin–Heidelberg–Tokyo, 1986, 621 pp. | MR

[8] Knyagina V. N., Monakhov V. S., “O perestanovochnosti silovskikh podgrupp s podgruppami Shmidta”, Trudy Instituta matematiki i mekhaniki UrO RAN, 16, no. 3, 2010, 130–139

[9] Berkovich Ya. G., “Uslovie, neobkhodimoe dlya sovpadeniya gruppy s kommutantom”, Izv. vuzov. Matematika, 1968, no. 8(75), 11–17 | MR | Zbl

[10] Monakhov V. S., “Razreshimost faktorizuemoi gruppy s razlozhimymi faktorami”, Mat. zametki, 34:3 (1983), 337–340 | MR | Zbl

[11] Romanovskii A. V., “Gruppy s khollovymi normalnymi delitelyami”, Konechnye gruppy, Nauka i tekhnika, Minsk, 1966, 98–115 | MR