The question of how certain arithmetical conditions on the lengths of the conjugacy classes of a finite group G influence the group structure has been studied by several authors with many results available. The purpose of this paper is to analyse the restrictions imposed by the lengths of the conjugacy classes of some elements of the factors of a finite group G = G1G2 · · · Gr, which is the product of the pairwise mutually permutable subgroups G1, G2, . . . , Gr, on its structure. Some earlier results appear as corollaries of our main theorems.
Finite groups Mutually permutable products Conjugacy classes