Abstract
Given a hereditary saturated formation F of soluble groups, we study finite groups with three F-subgroups of coprime indices. We obtain the new criteria for these groups to lie in the Shemetkov formations, the formations of all supersoluble groups, the formations of all groups with nilpotent commutator subgroup, and other formations.
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Original Russian Text Copyright © 2018 Vasil’ev A.F., Vasil’eva T.I., and Parfenkov K.L.
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 59, No. 1, pp. 65–77, January–February, 2018; DOI: 10.17377/smzh.2018.59.106
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Vasil’ev, A.F., Vasil’eva, T.I. & Parfenkov, K.L. Finite Groups with Three Given Subgroups. Sib Math J 59, 50–58 (2018). https://doi.org/10.1134/S0037446618010068
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DOI: https://doi.org/10.1134/S0037446618010068