Induced Characters From Linear Characters Of A π-Hall Subgroup

Induced character plays an important role in the character theory of finite groups. Applying the concept of induced character, we can investigate the irreducible characters of G by the irreducible characters of its subgroups. Linear character has special properties. We investigated the induced characters from linear characters of nilpotentπ-Hall subgroups.The main result of the paper is: Let G be a finite group with an abelianπ-Hall subgroup. Ifγ,μ∈Lin(H), thenγ~G =μ~G if and only ifγandμare N_G(H)-conjugate. It generalizes the theorem in [7] which was proved by Navarro.