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On Intersections of Certain Nilpotent Subgroups in Finite Groups
V. I. Zenkovab a N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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 $G$.
Keywords:
finite group, Abelian subgroup, nilpotent subgroup, intersection of subgroups, Fitting subgroup.
Received: 13.01.2022 Revised: 17.02.2022
Citation:
V. I. Zenkov, “On Intersections of Certain Nilpotent Subgroups in Finite Groups”, Mat. Zametki, 112:1 (2022), 55–60; Math. Notes, 112:1 (2022), 65–69
Linking options:
https://www.mathnet.ru/eng/mzm13418https://doi.org/10.4213/mzm13418 https://www.mathnet.ru/eng/mzm/v112/i1/p55
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Abstract page: | 148 | Full-text PDF : | 36 | References: | 35 | First page: | 2 |
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