On the Number of Characters in Blocks of Quasi-simple Groups
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We prove, for primes p ≥ 5, two inequalities between the fundamental invariants of Brauer p-blocks of finite quasi-simple groups: the number of characters in the block, the number of modular characters, the number of height 0 characters, and the number of conjugacy classes of a defect group and of its derived subgroup. For this, we determine these invariants explicitly, or at least give bounds for them for several classes of classical groups.
KeywordsNumber of simple modules Invariants of blocks Inequalities for blocks of simple groups
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I thank Frank Himstedt for providing me with information on the principal 2- and 3-blocks of 3D4(q), Donna Testerman for a careful reading of a preliminary version, as well as Zhicheng Feng and Sofia Brenner for some remarks and the anonymous referee for his help with the proper use of the English language and for pointing out three inaccuracies in a previous version of Table 2.
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