Book Section records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 06 Dec 2023 13:00:49 +0000Finite simple groups and their subgroups
https://resolver.caltech.edu/CaltechAUTHORS:20201001-145810955
Authors: Aschbacher, Michael
Year: 1986
DOI: 10.1007/bfb0076170
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.https://authors.library.caltech.edu/records/rddsk-b2514Some Multilinear Forms with Large Isometry Groups
https://resolver.caltech.edu/CaltechAUTHORS:20200930-113055093
Authors: Aschbacher, Michael
Year: 1988
DOI: 10.1007/978-94-009-4017-8_15
Many groups are best described as the group of automorphisms of some natural object. I'm interested in obtaining such descriptions of the finite simple groups, and more generally descriptions of the groups of Lie type over arbitrary fields. The representation of the alternating group of degree n as the group of automorphisms of a set of order n is an excellent example of such a description. The representation of the classical groups as the isometry groups of bilinear or sequilinear forms is another.https://authors.library.caltech.edu/records/efe7x-yvd92Quasithin Groups
https://resolver.caltech.edu/CaltechAUTHORS:20200512-081608756
Authors: Aschbacher, Michael
Year: 1998
DOI: 10.1007/978-94-011-5308-9_18
The treatment of quasithin groups of characteristic 2 was one of the last steps in the Classification of the finite simple groups. Geoff Mason [12] announced a classification of these groups in about 1980, but never published his work. A few people have a copy of a large manuscript containing his efforts, but because it was distributed slowly, section by section, it was only during the last few years that it was realized that Mason's manuscript is incomplete in various ways. A few years ago I wrote up a treatment which begins where Mason's manuscript ends and finishes the problem assuming the results he says he proves. I have only read Mason's manuscript superficially, but it appears there are missing lemmas even for the part of the problem the theorems in his manuscript cover. I do believe however that he has seriously addressed the issues involved and that he could turn his manuscript into a proof with enough work. However Mason is now involved with Moonshine and has no interest in completing or publishing his manuscript.https://authors.library.caltech.edu/records/g57yg-2jx07Quasithin Groups
https://resolver.caltech.edu/CaltechAUTHORS:20200512-100004286
Authors: Aschbacher, Michael G.; Smith, Stephen D.
Year: 1998
DOI: 10.1007/978-3-0348-8819-6_1
Geoff Mason announced in about 1980 the classifcication of quasithin groups of characteristic 2; but never published this step in the classification of the finite simple groups. In January 1996, the authors began work toward a new and more general classification of quasithin groups; the paper gives an exposition of the approach and considerable progress to date.https://authors.library.caltech.edu/records/ytern-gd019On a question of Farjoun
https://resolver.caltech.edu/CaltechAUTHORS:20180802-143851994
Authors: Aschbacher, Michael
Year: 2008
DOI: 10.1515/9783110198126.1
[no abstract]https://authors.library.caltech.edu/records/gst1n-3qv43The subgroup structure of finite groups
https://resolver.caltech.edu/CaltechAUTHORS:20170928-081918166
Authors: Aschbacher, Michael
Year: 2017
DOI: 10.1090/conm/694/13959
[No abstract]https://authors.library.caltech.edu/records/hv2fa-w5m79