Israel Journal of Mathematics

, Volume 151, Issue 1, pp 357–380 | Cite as

The exchange condition for association schemes

  • Paul-Hermann Zieschang


The present article generalizes the group-theoretical exchange condition to the theory of association schemes. We prove that a large class of association schemes satisfying our exchange condition arises from groups as quotients over subgroups. The result provides an alternate proof of Tits' reduction theorem for buildings of spherical type.


Exchange Condition Coxeter Group Association Scheme Reduction Theorem Spherical Type 
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Copyright information

© The Hebrew University Magnes Press 2006

Authors and Affiliations

  • Paul-Hermann Zieschang
    • 1
  1. 1.Department of MathematicsUniversity of Texas at BrownsvilleBrownsvilleUSA

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