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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 4, Pages 866–869
DOI: https://doi.org/10.33048/smzh.2022.63.412
(Mi smj7699)
 

On intersections of $\pi$-Hall subgroups in finite $D_\pi$-groups

V. I. Zenkov

N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
References:
Abstract: We give an example of a series of finite $D_\pi$-groups where for each group $G$ in the series and its $\pi$-Hall subgroup $H$, the inequality $H\cap H^x\cap H^y \neq1$ holds for all $x, y \in G$. Thus a negative answer is obtained both to Problem 7.3 by Vdovin and Revin and its analog—Question 18.31 in The Kourovka Notebook. We also describe the subgroups $\operatorname{Min}_G(H,H,H)$ and $\min_G(H,H,H)$.
Keywords: finite group, $D_\pi$-subgroup, intersection of subgroups.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00456
Ministry of Education and Science of the Russian Federation 02.А03.210006
The author was supported by the Russian Foundation for Basic Research (Grant no. 20–01–00456) and the Russian Academic Excellence Project (Agreement 02.A03.210006 of 27.08.2013).
Received: 20.10.2021
Revised: 20.10.2021
Accepted: 10.12.2021
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 4, Pages 720–722
DOI: https://doi.org/10.1134/S0037446622040127
Document Type: Article
UDC: 512.542
Language: Russian
Citation: V. I. Zenkov, “On intersections of $\pi$-Hall subgroups in finite $D_\pi$-groups”, Sibirsk. Mat. Zh., 63:4 (2022), 866–869; Siberian Math. J., 63:4 (2022), 720–722
Citation in format AMSBIB
\Bibitem{Zen22}
\by V.~I.~Zenkov
\paper On~intersections of~$\pi$-Hall~subgroups in finite $D_\pi$-groups
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 4
\pages 866--869
\mathnet{http://mi.mathnet.ru/smj7699}
\crossref{https://doi.org/10.33048/smzh.2022.63.412}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 4
\pages 720--722
\crossref{https://doi.org/10.1134/S0037446622040127}
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