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Mat. Zametki, 2019, Volume 105, Issue 3, Pages 383–394 (Mi mz11742)  

On Intersections of Abelian and Nilpotent Subgroups in Finite Groups. II

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: Let $G$ be a finite group, and let $A$ and $B$ be, respectively, an Abelian and a nilpotent subgroup in $G$. In the present paper, we complete the proof of the theorem claiming that there is an element $g$ of $G$ such that the intersection of $A$ with the subgroup conjugate to $B$ by $g$ is contained in the Fitting subgroup of $G$.

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

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 02.А03.210006
Ural Branch of the Russian Academy of Sciences 15-16-1-5
This work was supported by the State Budget Project “Current Problems of Algebra and Combinatorics” (no. 15-16-1-5) (Theorem 1) and by the Project of Increasing the Competitiveness of the Leading Universities of Russia (agreement 02. A03.210006 as of August 27, 2013) (Secs. 1–2 of the present paper).


DOI: https://doi.org/10.4213/mzm11742

Full text: PDF file (523 kB)
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UDC: 512.542
Received: 10.07.2017
Revised: 27.02.2018

Citation: V. I. Zenkov, “On Intersections of Abelian and Nilpotent Subgroups in Finite Groups. II”, Mat. Zametki, 105:3 (2019), 383–394

Citation in format AMSBIB
\Bibitem{Zen19}
\by V.~I.~Zenkov
\paper On Intersections of Abelian and Nilpotent Subgroups in Finite Groups.~II
\jour Mat. Zametki
\yr 2019
\vol 105
\issue 3
\pages 383--394
\mathnet{http://mi.mathnet.ru/mz11742}
\crossref{https://doi.org/10.4213/mzm11742}
\elib{http://elibrary.ru/item.asp?id=37045125}


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