This article is cited in 6 papers

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

V. I. Zenkov<sup>ab

a</sup> 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.

UDC: 512.542

Received: 10.07.2017
Revised: 27.02.2018

DOI: 10.4213/mzm11742

 English version: Mathematical Notes, 2019, 105:3, 366–375

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