Geodesic
The setk $K_p$ in some finite groups
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 81 (2023), pp. 5-13

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The study of the properties of the set $K_p$ consisting of elements of a non-Abelian group that commute with exactly $p$ elements of the group $G$ is continued. In particular, this question is considered for groups of order $p_1p_2\cdots p_k$, $k\geqslant 3$ and $p^2q$, where $p_i$, $q$ are prime numbers. It is also proved that the set $K_5$ is non-empty in the three-dimensional projective special linear group. This group has the same order as the alternating group $A_8$, in which the set $K_5$ is empty.
Mots-clés : group
Keywords: centralizer of an element, involution, Sylow and Hall subgroups. 
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     author = {A. I. Zabarina and E. A. Fomina},
     title = {The setk $K_p$ in some finite groups},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {5--13},
     publisher = {mathdoc},
     number = {81},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2023_81_a0/}
}
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A. I. Zabarina; E. A. Fomina. The setk $K_p$ in some finite groups. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 81 (2023), pp. 5-13. http://geodesic.mathdoc.fr/item/VTGU_2023_81_a0/