Geodesic
Finite groups with $\mathbb{P}$-subnormal biprimary subgroups
Trudy Instituta matematiki, Tome 21 (2013) no. 1, pp. 63-68 
V. N. Kniahina. Finite groups with $\mathbb{P}$-subnormal biprimary subgroups. Trudy Instituta matematiki, Tome 21 (2013) no. 1, pp. 63-68. http://geodesic.mathdoc.fr/item/TIMB_2013_21_1_a7/
@article{TIMB_2013_21_1_a7,
     author = {V. N. Kniahina},
     title = {Finite groups with $\mathbb{P}$-subnormal biprimary subgroups},
     journal = {Trudy Instituta matematiki},
     pages = {63--68},
     year = {2013},
     volume = {21},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2013_21_1_a7/}
}
TY  - JOUR
AU  - V. N. Kniahina
TI  - Finite groups with $\mathbb{P}$-subnormal biprimary subgroups
JO  - Trudy Instituta matematiki
PY  - 2013
SP  - 63
EP  - 68
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMB_2013_21_1_a7/
LA  - ru
ID  - TIMB_2013_21_1_a7
ER  - 
%0 Journal Article
%A V. N. Kniahina
%T Finite groups with $\mathbb{P}$-subnormal biprimary subgroups
%J Trudy Instituta matematiki
%D 2013
%P 63-68
%V 21
%N 1
%U http://geodesic.mathdoc.fr/item/TIMB_2013_21_1_a7/
%G ru
%F TIMB_2013_21_1_a7

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

In this paper we study finite groups with $\mathbb{P}$-subnormal biprimary dispersive subgroups. We prove that a group all of whose biprimary $p$-closed $pd$-subgroups are $\mathbb{P}$-subnormal is $p$-solvable, where $p$ is the largest prime divisor of the order of the group. We also prove that a group with biprimary $2$-nilpotent $\mathbb{P}$-subnormal $2d$-subgroups is solvable.

[1] Monakhov V. S., Vvedenie v teoriyu konechnykh grupp i ikh klassov, uchebnoe posobie, Vysheishaya shkola, Minsk, 2006

[2] Shemetkov L. A., Formatsii konechnykh grupp, Nauka, M., 1978

[3] Vasilev A. F., Vasileva T. I., Tyutyanov V. N., “O konechnykh gruppakh sverkhrazreshimogo tipa”, Sib. mat. zhurn., 51:6 (2010), 1270–1281 | MR | Zbl

[4] Kniahina V. N., Monakhov V. S., Finite groups with $\mathbb{P}$-subnormal 2-maximal subgroups, 18 May 2011, arXiv: 1105.3663 | MR

[5] Kniahina V. N., Monakhov V. S., Finite groups with $\mathbb{P}$-subnormal primary cyclic subgroups, 18 Nov 2011, arXiv: 1110.4720V2

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

[7] Vasilev A. F., Vasileva T. I., Tyutyanov V. N., “O konechnykh gruppakh, blizkikh k sverkhrazreshimym gruppam”, Problemy fiziki, matematiki i tekhniki, 2010, no. 2(3), 21–27 | MR

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