Higman Numbers of Finite Groups

In this article, the relation is clarified between the units of character fields and the central units of integer group rings. The notion of the Higman number of a finite group is introduced and several ways of finding the Higman numbers are analyzed. For various field classes, we derive exponents of unit groups of factor rings of the integer ring by principal ideals generated by naturals. On this basis, we obtain some results on divisibility of the Higman numbers.