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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
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.
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; Math. Notes, 105:3 (2019), 366–375
Linking options:
https://www.mathnet.ru/eng/mzm11742https://doi.org/10.4213/mzm11742 https://www.mathnet.ru/eng/mzm/v105/i3/p383
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