FINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES

Abstract

‎Let G be a finite group and Z(G) be the center of G‎. ‎For a subset A of G‎, ‎we define k_G(A)‎, ‎the number of conjugacy classes of G that intersect A non-trivially‎. ‎In this paper‎, ‎we verify the structure of all finite groups G which satisfy the property k_G(G-Z(G))=5, and classify them‎.