Geodesic
On the permutability of Sylow subgroups with derived subgroups of $B$-subgroups
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2019), pp. 12-17.

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A finite non-nilpotent group $G$ is called a $B$-group if every proper subgroup of the quotient group $G/\Phi(G)$ is nilpotent. We establish the $r$-solvability of the group in which some Sylow $r$-subgroup permutes with the derived subgroups of $2$-nilpotent (or $2$-closed) $B$-subgroups of even order and the solvability of the group in which the derived subgroups of $2$-closed and $2$-nilpotent $B$-subgroups of even order are permutable.
Keywords: finite group; $r$-solvable group; Sylow subgroup; $B$-group; the derived subgroup; permutable subgroups. 
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E. V. Zubei. On the permutability of Sylow subgroups with derived subgroups of $B$-subgroups. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2019), pp. 12-17. http://geodesic.mathdoc.fr/item/BGUMI_2019_1_a1/

[1] O. Yu. Shmidt, “Gruppy, vse podgruppy kotorykh spetsialnye”, Matematicheskii sbornik, 31(3–?4) (1924), 366–372

[2] N. F. Kuzennyi, S. S. Levischenko, “Konechnye gruppy Shmidta i ikh obobscheniya”, Ukrainskii matematichnii zhurnal, 43(7–8) (1991), 963–968

[3] V. S. Monakhov, “Podgruppy Shmidta, ikh suschestvovanie i nekotorye prilozheniya”, Trudy Ukrainskogo matematicheskogo kongressa: sbornik trudov, 2002, 81–90, Kiev: Institut matematiki NAN Ukrainy

[4] Ya. G. Berkovich, E. M. Palchik, “O perestanovochnosti podgrupp konechnoi gruppy”, Sibirskii matematicheskii zhurnal, 8(4) (1967), 741–753

[5] V. N. Knyagina, V. S. Monakhov, “O perestanovochnosti silovskikh podgrupp s podgruppami Shmidta”, Trudy Instituta matematiki i mekhaniki UrO RAN, 16(3) (2010), 130–139

[6] V. N. Knyagina, V. S. Monakhov, “O perestanovochnosti maksimalnykh podgrupp s podgruppami Shmidta”, Trudy Instituta matematiki i mekhaniki UrO RAN, 17(4) (2011), 126–133

[7] V. N. Knyagina, V. S. Monakhov, “O perestanovochnosti n-maksimalnykh podgrupp s podgruppami Shmidta”, Trudy Instituta matematiki i mekhaniki UrO RAN, 18(3) (2012), 125–130

[8] V. S. Monakhov, “O konechnykh gruppakh s zadannym naborom podgrupp Shmidta”, Matematicheskie zametki, 58(5) (1995), 717–722 | Zbl

[9] V. N. Knyagina, V. S. Monakhov, “O konechnykh gruppakh s nekotorymi cubnormalnymi podgruppami Shmidta”, Sibirskii matematicheskii zhurnal, 45(6) (2004), 1316–1322 | MR | Zbl

[10] V. N. Knyagina, V. S. Monakhov, “Konechnye gruppy s polunormalnymi podgruppami Shmidta”, Algebra i logika, 46(4) (2007), 448–458 | MR | Zbl

[11] V. A. Vedernikov, “Konechnye gruppy s subnormalnymi podgruppami Shmidta”, Algebra i logika, 46(6) (2007), 669–687 | Zbl

[12] V. N. Kniahina, V. S. Monakhov, “Finite groups with Hall Schmidt subgroups”, Publicationes Mathematicae Debrecen, 81(3–4) (2012), 341–350 | DOI | MR | Zbl

[13] KhA. Al-Sharo, A. N. Skiba, “On finite groups with s-subnormal Schmidt subgroups”, Communications in Algebra, 45(10) (2017), 4158–4165 | DOI | MR | Zbl

[14] Y. Berkovich, Z. Janko, “Groups of Prime Power Order”, Berlin: Walter de Gruyter, 2011 | MR | Zbl

[15] V. N. Knyagina, “O proizvedenii B-gruppy i primarnoi gruppy”, Problemy fiziki, matematiki i tekhniki, 3(32) (2017), 52–57 | MR | Zbl

[16] B. Huppert, “Endliche Gruppen I”, Berlin: Springer-Verlag, 1967 | DOI | MR | Zbl

[17] V. S. Monakhov, “Vvedenie v teoriyu konechnykh grupp i ikh klassov”, Minsk: Vysheishaya shkola, 2006

[18] V. S. Monakhov, “O podgruppakh Shmidta konechnykh grupp”, Voprosy algebry, 13 (1998), 153–171

[19] A. N. Skiba, “H-permutable subgroups”, Izvestiya Gomelskogo gosudarstvennogo universiteta, 4 (2003), 37–39

[20] W. Guo, K. P. Shum, A. N. Skiba, “X-semipermutable subgroups of finite groups”, Journal of Algebra, 315(1) (2007), 31–?41 | DOI | MR | Zbl

[21] V. P. Burichenko, “O gruppakh, elementy malykh poryadkov kotorykh porozhdayut maluyu podgruppu”, Matematicheskie zametki, 92(3) (2012), 361–367 | DOI | MR | Zbl