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Matematicheskie Zametki, 2019, Volume 105, Issue 3, Pages 383–394
DOI: https://doi.org/10.4213/mzm11742 (Mi mzm11742) 		 
This article is cited in 4 scientific papers (total in 4 papers)

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
Full-text PDF (523 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm11742
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).
Received: 10.07.2017
Revised: 27.02.2018
English version:
Mathematical Notes, 2019, Volume 105, Issue 3, Pages 366–375
DOI: https://doi.org/10.1134/S0001434619030076
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: V. I. Zenkov, “On Intersections of Abelian and Nilpotent Subgroups in Finite Groups. II”, Mat. Zametki, 105:3 (2019), 383–394; Math. Notes, 105:3 (2019), 366–375
Citation in format AMSBIB
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