Geodesic
On finite $\pi$-solvable groups with bicyclic Sylow subgroups
Problemy fiziki, matematiki i tehniki, no. 1 (2013), pp. 61-66 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 
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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