A class of blocks behaving like blocks of p-solvable groups

We define a class of blocks having similar properties to blocks of p-solvable groups, and show that a version of the Fong–Swan theorem holds for irreducible Brauer characters in such blocks. We also show that the height of an irreducible character in such block is bounded by the exponent of the central quotient of a defect group, which in particular implies that if further the defect groups are abelian, then every irreducible character in the block has height zero.