On the set K<sub>p</sub> in finite groups
The properties of the set Kp 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 Kp 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 К3 form one conjugacy class.