A Remark on the Construction of Centric Linking Systems

  • B. Oliver
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 242)


We give examples to show that it is not, in general, possible to prove the existence and uniqueness of centric linking systems associated to a given fusion system inductively by adding one conjugacy class at a time to the categories. This helps to explain why it was so difficult to prove that these categories always exist, and also helps to motivate the procedure used by Chermak [5] when he did prove it. It also shows that the claim by Puig [12] to have proven this result in a recently published paper is not correct.


Finite groups Sylow subgroups Fusion 

2000 Mathematics Subject Classification

Primary 20D20 Secondary 20D45 20E45 


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.LAGAUniversité Paris 13, Sorbonne Paris Cité, UMR 7539 du CNRSVilletaneuseFrance

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