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Gorenstein–Harada theorem

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In mathematical finite group theory, the Gorenstein–Harada theorem, proved by Gorenstein and Harada (1973, 1974) in a 464-page paper,[1] classifies the simple finite groups of sectional 2-rank at most 4. It is part of the classification of finite simple groups.[2]

Finite simple groups of section 2 that rank at least 5, have Sylow 2-subgroups with a self-centralizing normal subgroup of rank at least 3, which implies that they have to be of either component type or of characteristic 2 type. Therefore, the Gorenstein–Harada theorem splits the problem of classifying finite simple groups into these two sub-cases.

References

  1. ^ "Abc conjecture — The Enormity of Math". Medium, Cami Rosso, Feb 23, 2017
  2. ^ Bob Oliver (25 January 2016). Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4. American Mathematical Soc. pp. 1, 3. ISBN 978-1-4704-1548-8.