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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2018, Volume 15, Pages 21–28
DOI: https://doi.org/10.17377/semi.2018.15.003
(Mi semr894)
 

Mathematical logic, algebra and number theory

On intersection two nilpotent subgroups in small groups

V. I. Zenkovab

a Yeltsin Ural Federal University, Mira street, 19, 620990, Ekaterinburg, Russia
b N.N. Krasovskii Institute of Mathematics and Mechanics, S.Kovalevskoi street, 16, 620990, Ekaterinburg, Russia
References:
Abstract: In the paper we prove that if $G$ is a finite almost simple group with socle isomorphic to $G_2(3)$, $G_2(4)$, $F_4(2)$, ${}^2E_6(2)$, $Sz(8)$, then for every nilpotent subgroups $A,B$ of $G$ there exists an element $g\in G$ such that $A\cap B^g=1$, except the case $G=Aut(F_4(2))$, and $A,B$ are $2$-groups.
Keywords: finite group, simple group, nilpotent subgroup, intersection of subgroups.
Funding agency Grant number
Russian Science Foundation 15-11-10025
Received July 31, 2017, published January 18, 2018
Bibliographic databases:
Document Type: Article
UDC: 512.542
MSC: 20D06, 20D15
Language: Russian
Citation: V. I. Zenkov, “On intersection two nilpotent subgroups in small groups”, Sib. Èlektron. Mat. Izv., 15 (2018), 21–28
Citation in format AMSBIB
\Bibitem{Zen18}
\by V.~I.~Zenkov
\paper On intersection two nilpotent subgroups in small groups
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 21--28
\mathnet{http://mi.mathnet.ru/semr894}
\crossref{https://doi.org/10.17377/semi.2018.15.003}
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