The set Kp in some finite groups

Abstract

The study of the properties of the set Kp 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 p1p2...pk, k ≥ 3 and p2q, where рі, q are prime numbers. It is also proved that the set K5 is non-empty in the three-dimensional projective special linear group. This group has the same order as the alternating group A8, in which the set K5 is empty.