Geodesic
On $\pi$-solvability of a finite group with a partially permutable $\pi$-Hall subgroup
Problemy fiziki, matematiki i tehniki, no. 1 (2010), pp. 25-27.

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We investigate a finite group such that its $\pi$-Hall subgroup is permutable with some subgroups of the group. For instance, we establish $\pi$-solvability of such groups in two cases: a $\pi$-Hall subgroup is 2-nilpotent; a $\pi$-Hall subgroup is solvable and $3\notin\pi$. Besides, we establish solvability of a finite group in the case when a 2-nilpotent $\pi$-Hall subgroup of the group has odd index.
Keywords: finite group, seminormal subgroup, $\pi$-Hall subgroup
Mots-clés : $\pi$-solvable group. 
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V. N. Kniahina. On $\pi$-solvability of a finite group with a partially permutable $\pi$-Hall subgroup. Problemy fiziki, matematiki i tehniki, no. 1 (2010), pp. 25-27. http://geodesic.mathdoc.fr/item/PFMT_2010_1_a4/

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

[2] V. S. Monakhov, “Konechnye gruppy s polunormalnoi khollovoi podgruppoi”, Matematicheskie zametki, 80:4 (2006), 573–581 | DOI | MR | Zbl

[3] A. N. Skiba, “$H$-permutable subgroups”, Izvestiya Gomelskogo gos. un-ta im. F. Skoriny, 2003, no. 4 (19), 37–39

[4] L. A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978, 272 pp. | MR | Zbl

[4] V. S. Monakhov, “Proizvedenie razreshimoi i tsiklicheskoi grupp”, YI Vsesoyuznyi simpozium po teorii grupp, Sbornik nauchnykh trudov, ed. S. N. Chernikov, Navukova dumka, Kiev, 1980, 188–195 | MR

[5] S. A. Syskin, “Ob odnom voprose R. Bera”, Sibirskii matematicheskii zhurnal, 20:3 (1979), 679–681 | MR | Zbl