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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 21–28 (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

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


DOI: https://doi.org/10.17377/semi.2018.15.003

Full text: PDF file (164 kB)
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Document Type: Article
UDC: 512.542
MSC: 20D06, 20D15
Received July 31, 2017, published January 18, 2018

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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