Abstract
It is proved that, in any finite group \(G\) with nilpotent subgroups \(A\) and \(B\) and the condition \(A\cap B^g\unlhd\langle A,B^g\rangle\) for any \(g\) in \(G\), \(\operatorname{Min}_G(A,B)\) is a subgroup of \(F(G)\). This generalizes the author’s theorem about intersections of Abelian subgroups in a finite group, since this holds, for example, for Hamiltonian subgroups \(A\) and \(B\) in \(G\).
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Funding
This work was financially supported by the Russian Foundation for Basic Research (grant no. 20-01-00456) and by the Competitiveness Enhancement Program for Leading Universities of Russia (agreement 02. A03.210006 of 27.08.2013).
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Translated from Matematicheskie Zametki, 2022, Vol. 112, pp. 55–60 https://doi.org/10.4213/mzm13418.
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Zenkov, V.I. On Intersections of Certain Nilpotent Subgroups in Finite Groups. Math Notes 112, 65–69 (2022). https://doi.org/10.1134/S0001434622070069
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DOI: https://doi.org/10.1134/S0001434622070069