Let F be an unequal
characteristic local field. The aim of this paper is to outline a block form of the
Cartan-Brauer modular decomposition theory which incorporates the notion of defect
groups. The irreducible F-representations of a finite group G are associated with
blocks in the group algebra over the residue field F. The defect groups of a block to
which an irreducible F-representation T belongs are shown to coincide with the
defect groups of the block to which any absolutely irreducible constituent of T
belongs. A result on the Schur index of an absolutely irreducible representation
belonging to a block of defect zero is proven which yields an analogue to the
Brauer-Nesbitt Theorem on blocks of defect zero. The number of F-blocks of highest
defect is shown to be equal to the number of p-regular F-conjugacy classes of highest
defect.
