The set K_p in some finite groups

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 p₁p₂...p_k, k ≥ 3 and p²q, where р_і, 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.

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