Real 2-Regular Classes and 2-Blocks
Gow, Roderick and Murray, John (2000) Real 2-Regular Classes and 2-Blocks. Journal of Algebra, 230 (2). pp. 455-473. ISSN 0021-8693
Suppose that G is a finite group. We show that every 2-block of G has a defect class which is real. As a partial converse, we show that if G has a real 2-regular class with defect group D and if NŽD.D has no dihedral subgroup 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 give several applications of these results and also investigate some consequences of the existence of non-real 2-blocks.
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