Brauer Character Triples And Inductors

Brauer character triples and their inductors of finite groups are studied in this paper,and it is proved under some nilpotency condition that any two quasi-primitive inductors have the same degree.As an application,the question of when a given irreducible Brauer character has the same primitively inductive degree is investigated.Finally,the inductor correspondence of Brauer character triples is given.Our results generalize the corresponding theorems of Isaacs regarding complex character triples and their inductors.The main results of this thesis are as follows:Theorem A Suppose that G is a p-solvable group,and that T =(G,N,?)is a Brauer character triple.If N is nilpotent,then all quasiprimitive inductors of T have equal degrees.As an application,we obtain the following results.Theorem B Suppose that G is a p-solvable group and assume that the restriction?F(G)of ? ? IBr(G)on Fitting subgroup F(G)of G is irreducible.Then all primitive Brauer characters which induce ? have equal degrees.The corresponding theorem regarding Brauer character triples and their inductors is as follows.Theorem C Let G be a p-solvable group.Suppose that T =(G,N,?)is a Brauer character triple and that S =(H,M,?)is an inductor for T.If M is a subnormal subgroup of N,then induction of Brauer characters defines a bijection from IBr(H|?)onto IBr(G|?).