Charles Eaton
UMIST (soon to be University of Manchester)
We define \emph{strongly $p$-solvable} blocks, which generalize
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 a
strongly $p$-solvable 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.
Status:preprint