The Classification of the Finite Simple Groups, Number 7: Part III, Chapters 7-11: The Generic Case, Stages 3b and 4a, Daniel Gorenstein, Richard Lyons, Ronald Solomon

Автор: Daniel Gorenstein, Richard Lyons, Ronald Solomon
Название: The Classification of the Finite Simple Groups, Number 8: Part III, Chapters 12-17: The Generic Case, Completed
ISBN: 1470441896 ISBN-13(EAN): 9781470441890
Издательство: Mare Nostrum (Eurospan)
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Описание: This book completes a trilogy (Numbers 5, 7, and 8) of the series The Classification of the Finite Simple Groups treating the generic case of the classification of the finite simple groups. In conjunction with Numbers 4 and 6, it allows us to reach a major milestone in our series--the completion of the proof of the following theorem: Theorem O: Let G be a finite simple group of odd type, all of whose proper simple sections are known simple groups. Then either G is an alternating group or G is a finite group of Lie type defined over a field of odd order or G is one of six sporadic simple groups.Put another way, Theorem O asserts that any minimal counterexample to the classification of the finite simple groups must be of even type. The work of Aschbacher and Smith shows that a minimal counterexample is not of quasithin even type, while this volume shows that a minimal counterexample cannot be of generic even type, modulo the treatment of certain intermediate configurations of even type which will be ruled out in the next volume of our series.

Автор: Alastair J. Litterick
Название: On Non-Generic Finite Subgroups of Exceptional Algebraic Groups
ISBN: 1470428377 ISBN-13(EAN): 9781470428372
Издательство: Mare Nostrum (Eurospan)
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Описание: The study of finite subgroups of a simple algebraic group $G$ reduces in a sense to those which are almost simple. If an almost simple subgroup of $G$ has a socle which is not isomorphic to a group of Lie type in the underlying characteristic of $G$, then the subgroup is called non-generic. This paper considers non-generic subgroups of simple algebraic groups of exceptional type in arbitrary characteristic.