Geodesic
On $p$-supersolubility of a finite factorized group with prime indexes of factors
Problemy fiziki, matematiki i tehniki, no. 4 (2014), pp. 100-105.

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

Sufficient conditions for $p$-supersolubility of a finite group $G=AB$, where $A$ and $B$ have cyclic Sylow $p$-subgroups are received. In particular, the supersolubility of a finite group $G=AB$ providing that all Sylow subgroups of $A$ and $B$ arecyclic, and the indexes of $A$ and $B$ in the group $G$ are prime is proved.
Keywords: finite group, $p$-supersoluble group
Mots-clés : $p$-solvable group. 
@article{PFMT_2014_4_a14,
     author = {I. K. Chirik},
     title = {On $p$-supersolubility of a finite factorized group with prime indexes of factors},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {100--105},
     publisher = {mathdoc},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2014_4_a14/}
}
TY  - JOUR
AU  - I. K. Chirik
TI  - On $p$-supersolubility of a finite factorized group with prime indexes of factors
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2014
SP  - 100
EP  - 105
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2014_4_a14/
LA  - ru
ID  - PFMT_2014_4_a14
ER  - 
%0 Journal Article
%A I. K. Chirik
%T On $p$-supersolubility of a finite factorized group with prime indexes of factors
%J Problemy fiziki, matematiki i tehniki
%D 2014
%P 100-105
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2014_4_a14/
%G ru
%F PFMT_2014_4_a14
I. K. Chirik. On $p$-supersolubility of a finite factorized group with prime indexes of factors. Problemy fiziki, matematiki i tehniki, no. 4 (2014), pp. 100-105. http://geodesic.mathdoc.fr/item/PFMT_2014_4_a14/

[1] V. S. Monakhov, Vvedenie v teoriyu konechnykh grupp i ikh klassov, Vysheishaya shkola, Minsk, 2006, 207 pp.

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

[3] Ya. G. Berkovich, “O razreshimykh gruppakh konechnogo poryadka”, Matematicheskii sbornik, 74(116):1 (1967), 75–92 | MR | Zbl

[4] V. D. Mazurov, Zamechaniya o konechnykh gruppakh, Dep. v VINITI 27.02.74, No 404-74, Akad. nauk SSSR, Novosibirsk, 1974, 7 pp.; Сиб. матем. журн., 16:2 (1975), 413

[5] V. D. Chertok, “Ob odnom klasse razreshimykh grupp”, Sibirskii matematicheskii zhurnal, 10:3 (1969), 712–715 | MR

[6] V. S. Monakhov, “O chastichnoi sverkhrazreshimosti konechnoi faktorizuemoi gruppy”, Doklady NAN Belarusi, 45:3 (2001), 32–36 | MR

[7] M. Asaad, V. S. Monakhov, “Some sufficient conditions for a finite group to be supersolvable”, Acta Mathematica Hungarica, 135:1–2 (2012), 168–173 | DOI | MR | Zbl

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

[9] V. S. Monakhov, O. A. Shpyrko, “O nilpotentnoi $\pi$-dline maksimalnykh podgrupp konechnykh $\pi$-razreshimykh grupp”, Vestnik Moskovskogo gosuniversiteta im. M. V. Lomonosova. Matematika. Mekhanika, 2009, no. 6, 3–8

[10] I. V. Lemeshev, V. S. Monakhov, “O razreshimosti nekotorykh konechnykh primitivnykh grupp”, Problemy fiziki, matematiki, tekhniki, 10:1 (2012), 87–91 | Zbl

[11] V. S. Monakhov, E. E. Gribovskaya, “O maksimalnykh i silovskikh podgruppakh konechnykh razreshimykh grupp”, Matematicheskie zametki, 70:4 (2001), 603–612 | DOI | MR | Zbl

[12] R. M. Guralnick, “Subgroups of prime power index in a simple group”, J. Algebra, 81:2 (1983), 304–311 | DOI | MR | Zbl

[13] V. S. Monakhov, “O proizvedenii dvukh razreshimykh podgrupp s maksimalnym peresecheniem faktorov”, Mezhvedomstv. sb., Voprosy algebry, 1, Min-vo vyssh. i sr. spets. obr. BSSR, Gomelskii gos. un-t, eds. L. A. Shemetkov i dr., Universitetskoe, Minsk, 1985, 54–57 | MR

[14] J. C. Lennox, S. E. Stonehewer, Subnormal subgroups of groups, Clarendon Press, Oxford, 1987 | MR | Zbl

[15] GAP — Groups, Algorithms and Programming, Version 4.4.12, , The GAP Group, 2009 (20.12.2009) http://www.gap-system.org

[16] V. S. Monakhov, A. A. Trofimuk, “O konechnykh razreshimykh gruppakh fiksirovannogo ranga”, Sibirskii matematicheskii zhurnal, 52:5 (2011), 1123–1137 | MR | Zbl