Fong Characters Of Subgroups Of π-Separable Groups

Let G be an M-group and x be a Bπ-character of G. Suppose that N is a normal subgroup of G and H is a Hall π-subgroup of G. In this paper by discussing Fong characters of H N in N, we obtain a sufficient condition for decomposing the degree of x into the form x(l) = (1) (l) where a is a Fong character of H in G associated with x and is an irreducible constituent of the restriction of x to N- Furthermore, if is a Bπ-character of N and is an irreducible character of H N which is a Fong character of H n N in N associated with d, then under the condition IH( ) = IH( ) we obtain a mutually determined relation between the set of Fong characters of I over which are associated with Bπ- characters of T over d and the set of Fong characters of H over which are associated with Bπ- characters of G over d.