Supercharacters of unipotent and solvable groups

Abstract: The notion of the supercharacter theory was introduced by P.Diaconis and I.M.Isaaks in 2008. In this paper we review the main statements of the general theory, we observe the construction of supercharacter theory for algebra groups and the theory of basic characters for the unitriangular groups over the finite field. Basing on the previous papers of the author, we construct the supercharacter theory for the finite groups of triangular type. We characterize the structure of Hopf algebra of supercharacters for the triangular group over the finite field.