A subgroup H of a finite group G is called wide if each prime divisor of the order of G divides the order of H. We obtain a description of finite solvable groups without wide subgroups. It is shown that a finite solvable group with nilpotent wide subgroups contains a quotient group with respect to the hypercenter without wide subgroups.
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References
V. S. Monakhov, Introduction to the Theory of Finite Groups and Their Classes [in Russian], Vysheish. Shkola, Minsk (2006).
B. Huppert, Endliche Gruppen I, Springer, Berlin (1967).
S. S. Levishchenko, “Finite quasibiprimary groups,” in: Groups Specified by the Properties of the System of Subgroups [in Russian], Proc. of the Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (1979), pp. 83–97.
O. Yu. Shmidt, “Groups all subgroups of which are special,” Mat. Sb., 31, 366–372 (1924).
Q. Zhang and L. Wang, “Finite non-Abelian simple groups which contain a nontrivial semipermutable subgroup,” Algebra Colloq., 12, 301–307 (2005).
Kourovskaya Notebook: Unsolved Problems of the Group Theory [in Russian], Edition 18, Institute of Mathematics, Novosibirsk (2014).
V. S. Monakhov, “Finite \( \pi \)-solvable groups with Hall subgroups,” Mat. Zametki, 84, No. 3, 390–394 (2008).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 7, pp. 957–962, July, 2016.
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Monakhov, V.S., Sokhor, I.L. Finitely Solvable Groups with Nilpotent Wide Subgroups. Ukr Math J 68, 1091–1096 (2016). https://doi.org/10.1007/s11253-016-1279-1
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DOI: https://doi.org/10.1007/s11253-016-1279-1