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Finite simple groups and their subgroups

Aschbacher, Michael (1986) Finite simple groups and their subgroups. In: Group Theory, Beijing 1984. Lecture Notes in Mathematics. No.1185. Springer , Berlin, Heidelberg, pp. 1-57. ISBN 9783540164562.

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The material in this article corresponds roughly to the contents of six lectures given at the International Symposium on Group Theory at Peking University in September 1984. In essence the article describes the beginnings of a theory of permutation representations of finite groups based on the classifications of the finite simple groups. Chapter 3 is devoted to an outline of the Classification, with emphasis on recent efforts to improve the proof of the Classification Theorem. Chapters, 1, 2, and 6 discuss finite groups themselves, a notion of geometry due to J. Tits, and a class of group theoretical techniques introduced by B. Fischer. Each of these topics plays a role in the theory of permutation representations under discussion. The heart of the theory is the study of the subgroup structure of the finite simple groups. Certain results on this structure are described in Chapter 4 and 5.

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Additional Information:© Springer-Verlag 1986. The author would like to thank the organizers of the Peking Symposium, particularly Professor Hsio-Fu Tuan, for all their efforts which made the conference and this article possible. The author's work is partially supported by the National Science Foundation.
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Subject Keywords:Finite Group; Simple Group; Maximal Subgroup; Finite Simple Group; Permutation Representation
Series Name:Lecture Notes in Mathematics
Issue or Number:1185
Record Number:CaltechAUTHORS:20201001-145810955
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105732
Deposited By: George Porter
Deposited On:02 Oct 2020 15:18
Last Modified:16 Nov 2021 18:45

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