Geodesic
On $p$-supersoluble residual of a product of normal $p$-supersoluble subgroups
Trudy Instituta matematiki, Tome 23 (2015) no. 2, pp. 88-96.

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Let a finite group $G$ be a product of two normal $p$-supersoluble subgroups. We prove that the $p$-supersoluble residual of $G$ coincides with the $p$-nilpotent residual of the commutator subgroup of $G$. Hence it follows that the supersoluble residual of a product of normal supersoluble subgroups coincides with the nilpotent residual of the commutator subgroup. 
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V. S. Monakhov; I. K. Chirik. On $p$-supersoluble residual of a product of normal $p$-supersoluble subgroups. Trudy Instituta matematiki, Tome 23 (2015) no. 2, pp. 88-96. http://geodesic.mathdoc.fr/item/TIMB_2015_23_2_a11/

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

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

[3] Huppert B., “Monomialle darstellung endlicher gruppen”, Nagoya Math. J., 3 (1953), 93–94 | DOI | MR

[4] Baer R., “Classes of finite groups and their properties”, Illinois J. Math., 1 (1957), 115–187 | MR | Zbl

[5] Friesen D., “Products of normal supersolvable subgroups”, Proc. Amer. Math. Soc., 30:1 (1971), 46–48 | DOI | MR | Zbl

[6] Vasilev A.F., Vasileva T.I., “O konechnykh gruppakh, u kotorykh glavnye faktory yavlyayutsya prostymi gruppami”, Izv. vuzov. Matem., 1997, no. 11(426), 10–14 | MR | Zbl

[7] Monakhov V.S., Chirik I.K., “O $p$-sverkhrazreshimosti konechnoi faktorizuemoi gruppy s normalnymi somnozhitelyami”, Trudy Instituta matematiki i mekhaniki UrO RAN, 21, no. 3, 2015, 256–267 | MR

[8] Guo W., Kondratiev A. S., “New examples of finite non-supersolvable groups factored by two normal supersolvable subgroups”, International Conference “Mal'tsev meeting”. Collection of abstracts (Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, 2012), 95

[9] Guo W., Kondratiev A. S., “Finite minimal non-supersolvable groups decomposable into the product of two normal supersolvable subgroups”, Commun. Math. Stat., 3 (2015), 285–290 | DOI | MR | Zbl