Abstract
We prove that a finite group whose every maximal subgroup is simple or nilpotent is a Schmidt group. A group whose every maximal subgroup is simple or supersoluble can be nonsoluble, and in this case we prove that its chief series has the form 1 ⊂ K ⊆ G, K }~ PSL 2(p) for a suitable prime p, |G: K| ≤ 2.
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Original Russian Text Copyright © 2014 Monakhov V.S. and Tyutyanov V.N.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 3, pp. 553–561, May–June, 2014.
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Monakhov, V.S., Tyutyanov, V.N. On finite groups with given maximal subgroups. Sib Math J 55, 451–456 (2014). https://doi.org/10.1134/S0037446614030069
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DOI: https://doi.org/10.1134/S0037446614030069