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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 728–732 (Mi semr949)  

Mathematical logic, algebra and number theory

On intersections of primary subgroups pairs in finite group with socle $\Omega_{2n}^+(2^m)$

V. I. Zenkovab

a N.N. Krasovskii Institute of Mathematics and Mechanics, S.Kovalevskoi street, 16, 620049, Ekaterinburg, Russia
b Yeltsin Ural Federal University, Mira street, 19, Ekaterinburg, Russia

Abstract: In theorem 1 for $Soc(G) = \Omega_{2n}^+(2)$, $n \ge 3$ and $S \in Syl_2(G)$ subgroup $min_G(S,S) = \langle S \bigcap S^g | |S \bigcap S^g| is minimal \rangle$ is constructed. In theorem 2 it is proved that if $Soc(G) = \Omega_{2n}^+(2^m)$ and for primary subgroups $A$ and $B$ we have $min_G(A,B) \ne 1$, then $m=1$, we can assume that $A$ and $B$ are subgroups of $S \in Syl_2(G)$, $|G:Soc(G)|=2$, involution from $G-Soc(G)$ induces the graph automorphism on $Soc(G)$ and $min_G(S,S)\subseteq A\cap B$.

Keywords: finite group, nilpotent subgroup, intersection of subgroups.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 15-16-1-5
Ministry of Education and Science of the Russian Federation 02.А03.21.0006


DOI: https://doi.org/10.17377/semi.2018.15.058

Full text: PDF file (146 kB)
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Document Type: Article
UDC: 512.542
MSC: 13A99
Received June 20, 2017, published June 18, 2018

Citation: V. I. Zenkov, “On intersections of primary subgroups pairs in finite group with socle $\Omega_{2n}^+(2^m)$”, Sib. Èlektron. Mat. Izv., 15 (2018), 728–732

Citation in format AMSBIB
\Bibitem{Zen18}
\by V.~I.~Zenkov
\paper On intersections of primary subgroups pairs in finite group with socle $\Omega_{2n}^+(2^m)$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 728--732
\mathnet{http://mi.mathnet.ru/semr949}
\crossref{https://doi.org/10.17377/semi.2018.15.058}


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