Real 2-regular classes and 2-blocks

Suppose that G is a finite group. We show that every 2-block of G has a def ect class which is real. As a partial converse, we show that if G has a rea l 2-regular class with defect group D and if N(D)/D has no dihedral subgrou p of order 8, then G has a real 2-block with defect group D. More generally , we show that every 2-block of G which is weakly regular relative to some normal subgroup N has a defect class which is real and contained in N. We g ive several applications of these results and also investigate some consequ ences of the existence of non-real 2-blocks. (C) 2000 Academic Press.