Geodesic
On the set $K_{p}$ in finite groups
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 68 (2020), pp. 33-40

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The properties of the set $K_{p}$ consisting of elements of a non-Abelian group commuting with exactly $p$ elements of the group are considered. In particular, the properties of the set $K_{p}$ in permutation groups and some solvable groups. One more proof is given that all involutions of a finite simple non-Abelian group $G$ with a nonempty set $K_{3}$ form one conjugacy class.
Mots-clés : group
Keywords: centralizer of an element, involution, Sylow and Hall subgroups. 
@article{VTGU_2020_68_a2,
     author = {A. I. Zabarina and E. A. Fomina},
     title = {On the set $K_{p}$ in finite groups},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {33--40},
     publisher = {mathdoc},
     number = {68},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2020_68_a2/}
}
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A. I. Zabarina; E. A. Fomina. On the set $K_{p}$ in finite groups. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 68 (2020), pp. 33-40. http://geodesic.mathdoc.fr/item/VTGU_2020_68_a2/