Blocks with equal height zero degrees

Malle, Gunter; Navarro, Gabriel

doi:10.1090/S0002-9947-2011-05333-X

Blocks with equal height zero degrees
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by Gunter Malle and Gabriel Navarro PDF

Trans. Amer. Math. Soc. 363 (2011), 6647-6669 Request permission

Abstract:

We investigate a natural class of blocks of finite groups: the blocks such that all of their height zero characters have the same degree. It is conceivable that these blocks, which are globally defined, are exactly the Broué-Puig (locally defined) nilpotent blocks and we offer some partial results in this direction. The most difficult result here is to prove that, with one family of possible exceptions, blocks with equal height zero degrees of simple groups have abelian defect groups and are in fact nilpotent.

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