The Classification of the Finite Simple Groups, Number 10 : Part V, Chapters 9-17: Theorem $C_6$ and Theorem $C^*_4$, Case a (Mathematical Surveys and Monographs)

Capdeboscq, Inna/ Gorenstein, Daniel/ Lyons, Richard

American Mathematical Society（2023/12発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 570 p.
• 言語 ENG
• 商品コード 9781470475536

Full Description

This book is 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. Specifically, this book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series (see SURV/40.9). This is a fascinating set of simple groups which have properties in common with matrix groups (or, more generally, groups of Lie type) defined both over fields of characteristic 2 and over fields of characteristic 3. This set includes 11 of the celebrated 26 sporadic simple groups along with several of their large simple subgroups. Together with SURV/40.9, this volume provides the first unified treatment of this class of simple groups.

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