The classification of the finite simple groups
著者
書誌事項
The classification of the finite simple groups
（Mathematical surveys and monographs, v. 40,
American Mathematical Society, c2021
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注記
Other authors: Daniel Gorenstein, Richard Lyons, Ronald Solomon
No. 9: pt. 5, chapters 1-8: theorem C5 and theorem C6, stage 1
Includes bibliographical references (p. 515-517) and index
内容説明・目次
内容説明
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.
目次
Introduction to theorem $\mathscr{C}_5$
General group-theoretic lemmas, and recognition theorems
Theorem $\mathscr{C}_5$: Stage 1
Theorem $\mathscr{C}_5$: Stage 2
Theorem $\mathscr{C}_5$
State 3
Theorem $\mathcal{C}_5$: Stage 4
Theorem $\mathscr{C}^*_6$: Stage 1
Preliminary properties of $\mathscr{K}$-groups
Bibliography
Index
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