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This article is cited in 1 scientific paper (total in 1 paper)
On the intersections of nilpotent subgroups in finite groups with socle $L_3(q)$ or $U_3(q)$
V. I. Zenkovab a 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:
Earlier, the author described up to conjugation all pairs $(A,B)$ of nilpotent subgroups $A$ and $B$ in a finite group $G$ with socle $L_2(q)$ for which $A\cap B^g\ne 1$ for any element $g$ of $G$. A similar description was obtained later by the author for primary subgroups $A$ and $B$ of a finite group $G$ with socle $L_n(2^m)$. In this paper, we describe up to conjugation all pairs $(A,B)$ of nilpotent subgroups $A$ and $B$ of a finite group $G$ with socle $L_3(q)$ or $U_3(q)$ for which $A\cap B^g\ne 1$ for any element $g$ of $G$. The obtained results confirm in the considered cases the hypothesis that for a finite simple non-Abelian group $G$ and its nilpotent subgroup $N$ there is an element $g\in G$ such that $N\cap N^g=1$ (Problem 15.40 from “The Kourovka Notebook”).
Keywords:
finite group, nilpotent subgroup, intersection of subgroups, Fitting subgroup.
Received: 22.09.2020 Revised: 20.12.2020 Accepted: 11.01.2021
Citation:
V. I. Zenkov, “On the intersections of nilpotent subgroups in finite groups with socle $L_3(q)$ or $U_3(q)$”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 1, 2021, 70–78
Linking options:
https://www.mathnet.ru/eng/timm1791 https://www.mathnet.ru/eng/timm/v27/i1/p70
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Abstract page: | 148 | Full-text PDF : | 31 | References: | 22 | First page: | 1 |
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