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Classification of Finite Simple Groups

Table of Contents

1. Overview

This is usually given as the world record for longest proof. The first proof took around 15000 pages in over a decade of journal articles. The second generation proof (by Gorenstein, Lyons, and Solomon) is still in progress, and should take around 7000 pages. Although daunting, it involves extraordinarily beautiful mathematics.

Aschbacher, in his article "The Status of the Classification of the Finite Simple Groups" (2004) has called the work on the classification problem by Ulrich Meierfrankenfeld, Bernd Stellmacher, Gernot Stroth, and a few others, a third generation program using the amalgam method as the main tool. This works appears to be on Stroth's website and continued on Meierfrankenfeld's site (See also arXiv:1906.07216.)

2. References

2.1. Second Generation Proof

This is a series of books published by AMS.

  • Daniel Gorenstein and Richard Lyons and Ronald Solomon,
    The classification of the finite simple groups.
    Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, 1994.
  • Daniel Gorenstein and Richard Lyons and Ronald Solomon,
    The classification of the finite simple groups, Number 2.
    Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, 1996.
  • Daniel Gorenstein and Richard Lyons and Ronald Solomon,
    The classification of the finite simple groups, Number 3.
    Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, 1998.
  • Daniel Gorenstein and Richard Lyons and Ronald Solomon,
    The classification of the finite simple groups, Number 4. Part II, Chapters 1-4: Uniqueness Theorems.
    Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, 1999.
  • Daniel Gorenstein and Richard Lyons and Ronald Solomon,
    The classification of the finite simple groups, Number 5.
    Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, 2002.
  • Daniel Gorenstein and Richard Lyons and Ronald Solomon,
    The classification of the finite simple groups, Number 6: Part IV: The Special Odd Case.
    Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, 2005.
  • Daniel Gorenstein and Richard Lyons and Ronald Solomon,
    The classification of the finite simple groups, Number 7: Part III, Chapters 7–11: The Generic Case, Stages 3b and 4a.
    Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, 2018
  • Daniel Gorenstein and Richard Lyons and Ronald Solomon,
    The Classification of the Finite Simple Groups, Number 8: Part III, Chapters 12–17: The Generic Case, Completed.
    Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, 2018.
  • Inna Capdeboscq and Daniel Gorenstein and Richard Lyons and Ronald Solomon,
    The Classification of the Finite Simple Groups, Number 9: Part V, Chapters 1-8: Theorem \(C_{5}\) and Theorem \(C_{6}\), Stage 1. Mathematical Surveys and Monographs, vol. 40, Providence, R.I.: American Mathematical Society, 2021

Last Updated 2022-02-14 Mon 14:50.