On finite $\pi$-solvable groups with bicyclic Sylow subgroups
Problemy fiziki, matematiki i tehniki, no. 1 (2013), pp. 61-66.

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

The group is called a bicyclic group if it is the product of two cyclic subgroups. It is proved that the $\pi$-solvable group with bicyclic Sylow $\pi$-subgroups for any $p\in\pi$ is at most 6 and if $2\notin\pi$, then the derived $\pi$-length of a $\pi$-solvable group with bicyclic Sylow $\pi$-subgroups for any $p\in\pi$ is at most 3.
Keywords: finite group, bicyclic group, Sylow subgroup, derived $\pi$-length.
Mots-clés : $\pi$-solvable group
@article{PFMT_2013_1_a10,
     author = {D. V. Gritsuk and V. S. Monakhov and O. A. Shpyrko},
     title = {On finite $\pi$-solvable groups with bicyclic {Sylow} subgroups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {61--66},
     publisher = {mathdoc},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2013_1_a10/}
}
TY  - JOUR
AU  - D. V. Gritsuk
AU  - V. S. Monakhov
AU  - O. A. Shpyrko
TI  - On finite $\pi$-solvable groups with bicyclic Sylow subgroups
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2013
SP  - 61
EP  - 66
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2013_1_a10/
LA  - ru
ID  - PFMT_2013_1_a10
ER  - 
%0 Journal Article
%A D. V. Gritsuk
%A V. S. Monakhov
%A O. A. Shpyrko
%T On finite $\pi$-solvable groups with bicyclic Sylow subgroups
%J Problemy fiziki, matematiki i tehniki
%D 2013
%P 61-66
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2013_1_a10/
%G ru
%F PFMT_2013_1_a10
D. V. Gritsuk; V. S. Monakhov; O. A. Shpyrko. On finite $\pi$-solvable groups with bicyclic Sylow subgroups. Problemy fiziki, matematiki i tehniki, no. 1 (2013), pp. 61-66. http://geodesic.mathdoc.fr/item/PFMT_2013_1_a10/

[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, Berlin–Heidelberg–New York, 1967 | Zbl

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

[4] V. S. Monakhov, A. A. Trofimuk, “On a Finite Group Having a Normal Series Whose Factors Have Bicyclic Sylow Subgroups”, Communications in Algebra, 39:9 (2011), 3178–3186 | MR | Zbl

[5] P. Hall, G. Higman, “The $p$-lengh of a $p$-soluble groups and reduction theorems for Burnside's problem”, Proc. London Math. Soc., 3:7 (1956), 1–42 | MR | Zbl

[6] A. Ballester-Bolinches, R. Estaban-Romero, M. Asaad, Products finite groups, De Gruyter Expositions in Mathematics, 2010, 53 pp.

[7] V. S. Monakhov, O. A. Shpyrko, “O nilpotentnoi $\pi$-dline konechnoi $\pi$-razreshimoi gruppy”, Diskretnaya matematika, 13:3 (2001), 145–152 | MR | Zbl