Relative partial characters and relative blocks of p-solvable groups

Suppose that G is a finite p-solvable group and let N be a normal subgroup. Let μ∈Irr(N) with inertial group T in G. Suppose μ extends to a subgroup R of T containing N such that R/N is a Sylow p-subgroup of the quotient group T/N. We show that the set Irr(G|μ) of irreducible characters of G lying over μ can be partitioned into “μ-blocks” which behave like the classical Brauer p-blocks. We also establish a “well behaved” one-to-one correspondence between the μ-blocks of G and certain Brauer p-blocks of a central extension of T/N by a p′-subgroup.