Journal of Automated Reasoning

, Volume 23, Issue 3, pp 235–264

A Formal Proof of Sylow's Theorem

  • Florian Kammüller
  • Lawrence C. Paulson

DOI: 10.1023/A:1006269330992

Cite this article as:
Kammüller, F. & Paulson, L.C. Journal of Automated Reasoning (1999) 23: 235. doi:10.1023/A:1006269330992


The theorem of Sylow is proved in Isabelle HOL. We follow the proof by Wielandt that is more general than the original and uses a nontrivial combinatorial identity. The mathematical proof is explained in some detail, leading on to the mechanization of group theory and the necessary combinatorics in Isabelle. We present the mechanization of the proof in detail, giving reference to theorems contained in an appendix. Some weak points of the experiment with respect to a natural treatment of abstract algebraic reasoning give rise to a discussion of the use of module systems to represent abstract algebra in theorem provers. Drawing from that, we present tentative ideas for further research into a section concept for Isabelle.

Sylow's theorem Isabelle theorem proving 

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Florian Kammüller
    • 1
  • Lawrence C. Paulson
    • 1
  1. 1.Computer LaboratoryUniversity of CambridgeUK

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