The Classification of the Finite Simple Groups, Number 8: Part III, Chapters 12-17: The Generic Case, Completed, Daniel Gorenstein, Richard Lyons, Ronald Solomon

Автор: Daniel Gorenstein, Richard Lyons, Ronald Solomon
Название: The Classification of the Finite Simple Groups, Number 7: Part III, Chapters 7-11: The Generic Case, Stages 3b and 4a
ISBN: 082184069X ISBN-13(EAN): 9780821840696
Издательство: Mare Nostrum (Eurospan)
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Описание: The classification of finite simple groups is a landmark result of modern mathematics. The multipart series of monographs which is being published by the AMS (Volume 40.1-40.7 and future volumes) represents the culmination of a century-long project involving the efforts of scores of mathematicians published in hundreds of journal articles, books, and doctoral theses, totaling an estimated 15,000 pages. This part 7 of the series is the middle of a trilogy (Volume 40.5, Volume 40.7, and forthcoming Volume 40.8) treating the Generic Case, i.e., the identification of the alternating groups of degree at least 13 and most of the finite simple groups of Lie type and Lie rank at least 4. Moreover, Volumes 40.4-40.8 of this series will provide a complete treatment of the simple groups of odd type, i.e., the alternating groups (with two exceptions) and the groups of Lie type defined over a finite field of odd order, as well as some of the sporadic simple groups. In particular, this volume completes the construction, begun in Volume 40.5, of a collection of neighboring centralizers of a particularly nice form. All of this is then applied to complete the identification of the alternating groups of degree at least 13.The book is suitable for graduate students and researchers interested in the theory of finite groups.

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.