The Classification of the Finite Simple Groups, Number 9: Part V, Chapters 1-8: Theorem $C_5$ and Theorem $C_6$, Stage 1

The Classification of the Finite Simple Groups, Number 9: Part V, Chapters 1-8: Theorem $C_5$ and Theorem $C_6$, Stage 1
ISBN-10
1470464373
ISBN-13
9781470464370
Category
Mathematics
Pages
520
Language
English
Published
2021-02-22
Publisher
American Mathematical Society
Authors
Richard Lyons, Ronald Solomon, Daniel Gorenstein

Description

This book is the ninth volume in a series whose goal is to furnish a careful and largely self-contained proof of the classification theorem for the finite simple groups. Having completed the classification of the simple groups of odd type as well as the classification of the simple groups of generic even type (modulo uniqueness theorems to appear later), the current volume begins the classification of the finite simple groups of special even type. The principal result of this volume is a classification of the groups of bicharacteristic type, i.e., of both even type and of $p$-type for a suitable odd prime $p$. It is here that the largest sporadic groups emerge, namely the Monster, the Baby Monster, the largest Conway group, and the three Fischer groups, along with six finite groups of Lie type over small fields, several of which play a major role as subgroups or sections of these sporadic groups.

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