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Nilpotent Blocks of Quasisimple Groups for the Prime Two

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Abstract

We examine nilpotency amongst blocks of positive defect of the quasisimple groups for the prime 2. We show that every nilpotent block of a quasisimple group has abelian defect groups, and prove a conjecture of Puig concerning the recognition of nilpotent blocks in the case of quasisimple groups. Explicit characterisations of nilpotent blocks are given for the classical, alternating and sporadic simple groups.

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Authors and Affiliations

  1. Department of Mathematics, University of Auckland, Auckland, New Zealand

    Jianbei An

  2. School of Mathematics, University of Manchester, Manchester, UK

    Charles William Eaton

Authors
  1. Jianbei An
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  2. Charles William Eaton
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Correspondence to Charles William Eaton.

Additional information

The first author is supported by the Marsden Fund (of New Zealand), via award number UOA 0721 and the second author is supported by a Royal Society University Research Fellowship.

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An, J., Eaton, C.W. Nilpotent Blocks of Quasisimple Groups for the Prime Two. Algebr Represent Theor 16, 1–28 (2013). https://doi.org/10.1007/s10468-011-9290-6

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