About the higman numbers of groups $L_2(2^n)$

In this article we study the relations between the units of character fields and the central units of integer group rings. The object of interest in this paper is finding of the exponents of unit groups of factor rings of the integer rings by principal ideals generated by natural numbers. In some cases we obtain the exact values of such exponents, and in the remaining cases their upper bounds. This leads to some results on divisibility of the Higman numbers.