Archiv der Mathematik

, Volume 94, Issue 5, pp 405–410 | Cite as

Realizing a fusion system by a single finite group

Article

Abstract

We show that every saturated fusion system can be realized as a full subcategory of the fusion system of a finite group. The result suggests the definition of an ‘exoticity index’ and raises some other questions which we discuss.

Mathematics Subject Classification (2000)

20C20 

Keywords

Fusion systems Exotic fusion systems Exoticity index 

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References

  1. 1.
    C. Broto, R. Levi, and B. Oliver, The homotopy theory of fusion systems, J. Amer. Math. Soc. 16 (2003), 779–856 (electronic).Google Scholar
  2. 2.
    Leary I.J., Stancu R.: Realising fusion systems. Algebra Number Theory 1, 17–34 (2007)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    L. Puig, Frobenius categories versus Brauer blocks, Progress in Mathematics, 274, Birkhäuser, Basel, 2009, The Grothendieck group of the Frobenius cateogry of a Brauer block.Google Scholar
  4. 4.
    K. Ragnarsson and R. Stancu, Saturated fusion systems as idempotents in the double Burnside ring, preprint.Google Scholar
  5. 5.
    Robinson G.R.: Amalgams, blocks, weights, fusion systems and finite simple groups. J. Algebra 314, 912–923 (2007)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    R. Stancu, Equivalent definitions of fusion systems, preprint (2003).Google Scholar

Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of AberdeenAberdeenUnited Kingdom

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