Geodesic
On $p$-supersoluble residual of a product of normal $p$-supersoluble subgroups
Trudy Instituta matematiki, Tome 23 (2015) no. 2, pp. 88-96 
V. S. Monakhov; I. K. Chirik. On $p$-supersoluble residual of a product of normal $p$-supersoluble subgroups. Trudy Instituta matematiki, Tome 23 (2015) no. 2, pp. 88-96. http://geodesic.mathdoc.fr/item/TIMB_2015_23_2_a11/
@article{TIMB_2015_23_2_a11,
     author = {V. S. Monakhov and I. K. Chirik},
     title = {On $p$-supersoluble residual of a product of normal $p$-supersoluble subgroups},
     journal = {Trudy Instituta matematiki},
     pages = {88--96},
     year = {2015},
     volume = {23},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2015_23_2_a11/}
}
TY  - JOUR
AU  - V. S. Monakhov
AU  - I. K. Chirik
TI  - On $p$-supersoluble residual of a product of normal $p$-supersoluble subgroups
JO  - Trudy Instituta matematiki
PY  - 2015
SP  - 88
EP  - 96
VL  - 23
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMB_2015_23_2_a11/
LA  - ru
ID  - TIMB_2015_23_2_a11
ER  - 
%0 Journal Article
%A V. S. Monakhov
%A I. K. Chirik
%T On $p$-supersoluble residual of a product of normal $p$-supersoluble subgroups
%J Trudy Instituta matematiki
%D 2015
%P 88-96
%V 23
%N 2
%U http://geodesic.mathdoc.fr/item/TIMB_2015_23_2_a11/
%G ru
%F TIMB_2015_23_2_a11

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

Let a finite group $G$ be a product of two normal $p$-supersoluble subgroups. We prove that the $p$-supersoluble residual of $G$ coincides with the $p$-nilpotent residual of the commutator subgroup of $G$. Hence it follows that the supersoluble residual of a product of normal supersoluble subgroups coincides with the nilpotent residual of the commutator subgroup.

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

[2] Huppert B., Endliche Gruppen I, Springer, Berlin–Heidelberg–New York, 1967 | MR | Zbl

[3] Huppert B., “Monomialle darstellung endlicher gruppen”, Nagoya Math. J., 3 (1953), 93–94 | DOI | MR

[4] Baer R., “Classes of finite groups and their properties”, Illinois J. Math., 1 (1957), 115–187 | MR | Zbl

[5] Friesen D., “Products of normal supersolvable subgroups”, Proc. Amer. Math. Soc., 30:1 (1971), 46–48 | DOI | MR | Zbl

[6] Vasilev A.F., Vasileva T.I., “O konechnykh gruppakh, u kotorykh glavnye faktory yavlyayutsya prostymi gruppami”, Izv. vuzov. Matem., 1997, no. 11(426), 10–14 | MR | Zbl

[7] Monakhov V.S., Chirik I.K., “O $p$-sverkhrazreshimosti konechnoi faktorizuemoi gruppy s normalnymi somnozhitelyami”, Trudy Instituta matematiki i mekhaniki UrO RAN, 21, no. 3, 2015, 256–267 | MR

[8] Guo W., Kondratiev A. S., “New examples of finite non-supersolvable groups factored by two normal supersolvable subgroups”, International Conference “Mal'tsev meeting”. Collection of abstracts (Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, 2012), 95

[9] Guo W., Kondratiev A. S., “Finite minimal non-supersolvable groups decomposable into the product of two normal supersolvable subgroups”, Commun. Math. Stat., 3 (2015), 285–290 | DOI | MR | Zbl