Abstract
Under study is the conjecture that for every three nilpotent subgroups A, B, and C of a finite group G there are elements x and y such that A ∩ Bx ∩ Cy ≤ F(G), where F(G) is the Fitting subgroup of G. We prove that a counterexample of minimal order to this conjecture is an almost simple group. The proof uses the classification of finite simple groups.
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Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 4, pp. 777–786.
The author was supported by the Complex Program of Fundamental Research of the Ural Branch of the Russian Academy of Sciences (Project 18-1-1-17) and the Russian Academic Excellence Project (Agreement 02.A03.210006 of 27.08.2013 between the Ministry of Education and Science of the Russian Federation and Ural Federal University).
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Zenkov, V.I. Intersections of Three Nilpotent Subgroups of Finite Groups. Sib Math J 60, 605–612 (2019). https://doi.org/10.1134/S0037446619040062
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DOI: https://doi.org/10.1134/S0037446619040062