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Real 2-Regular Classes and 2-Blocks

✍ Scribed by Roderick Gow; John Murray

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 136 KB
Volume: 230
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8321

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✦ Synopsis

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 Ž . class with defect group D and if N D rD 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. ᮊ 2000 Academic Press 4 defect zero. However, Theorem 4.8 establishes the following partial con-Ž . verse: Let D be a 2-subgroup of G and let N D denote its normalizer in 1 The second author was supported by a Forbairt Postdoctoral Grant while writing this paper.

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