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The structure of blocks with a Klein four defect group

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Abstract

We prove Erdmann’s conjecture (J Algebra 76:505–518, 1982) stating that every block with a Klein four defect group has a simple module with trivial source, and deduce from this that Puig’s finiteness conjecture holds for source algebras of blocks with a Klein four defect group. The proof uses the classification of finite simple groups.

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, 24-29 St. Giles’, Oxford, OX1 3LB, UK

    David A. Craven

  2. School of Mathematics, The University of Manchester, Alan Turing Building, Oxford Road, Manchester, M13 9PL, UK

    Charles W. Eaton

  3. Institute of Mathematics, King’s College, University of Aberdeen, Fraser Noble Building, Aberdeen, AB24 3UE, Scotland, UK

    Radha Kessar & Markus Linckelmann

Authors
  1. David A. Craven
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  2. Charles W. Eaton
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  3. Radha Kessar
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  4. Markus Linckelmann
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Correspondence to Markus Linckelmann.

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Craven, D.A., Eaton, C.W., Kessar, R. et al. The structure of blocks with a Klein four defect group. Math. Z. 268, 441–476 (2011). https://doi.org/10.1007/s00209-010-0679-4

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  • DOI: https://doi.org/10.1007/s00209-010-0679-4

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