Geodesic
On Intersections of Abelian and Nilpotent Subgroups in Finite Groups.~II
Matematičeskie zametki, Tome 105 (2019) no. 3, pp. 383-394

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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. 
@article{MZM_2019_105_3_a5,
     author = {V. I. Zenkov},
     title = {On {Intersections} of {Abelian} and {Nilpotent} {Subgroups} in {Finite} {Groups.~II}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {383--394},
     publisher = {mathdoc},
     volume = {105},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a5/}
}
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V. I. Zenkov. On Intersections of Abelian and Nilpotent Subgroups in Finite Groups.~II. Matematičeskie zametki, Tome 105 (2019) no. 3, pp. 383-394. http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a5/