Description

Book Synopsis
The tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. This book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series.

Table of Contents
  • General group-theoretic lemmas
  • Theorem $\mathscr{C}_6$ and $\mathscr{C}_6^*$
  • Theorems $\mathscr{C}_4$ and $\mathscr{C}_4^*$: Introduction
  • Theorem $\mathscr{C}_4^*$: Stage A1. First steps
  • Theorem $\mathscr{C}_4^*$: Stage A2. Nonconstrained $p$-rank 3 centralizers
  • Theorem $\mathscr{C}_4^*$: Stage A3. $KM$-singularities
  • Theorem $\mathscr{C}_4^*$: Stage A4. Setups for recognizing $G$
  • Theorem $\mathscr{C}_4^*$: Stage A5. Recognition
  • Properties of $\mathscr{K}$-groups
  • Bibliography
  • Index

The Classification of the Finite Simple Groups

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    A Paperback by Inna Capdeboscq, Daniel Gorenstein, Richard Lyons

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      Publisher: MP-AMM American Mathematical
      Publication Date: Publication Date: 12/31/2023 12:00:00 AM
      ISBN13: 9781470475536, 978-1470475536
      ISBN10: 1470475537
      Also in:
      Algebraic geometry

      Description

      Book Synopsis
      The tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. This book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series.

      Table of Contents
      • General group-theoretic lemmas
      • Theorem $\mathscr{C}_6$ and $\mathscr{C}_6^*$
      • Theorems $\mathscr{C}_4$ and $\mathscr{C}_4^*$: Introduction
      • Theorem $\mathscr{C}_4^*$: Stage A1. First steps
      • Theorem $\mathscr{C}_4^*$: Stage A2. Nonconstrained $p$-rank 3 centralizers
      • Theorem $\mathscr{C}_4^*$: Stage A3. $KM$-singularities
      • Theorem $\mathscr{C}_4^*$: Stage A4. Setups for recognizing $G$
      • Theorem $\mathscr{C}_4^*$: Stage A5. Recognition
      • Properties of $\mathscr{K}$-groups
      • Bibliography
      • Index

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