Book records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 06 Dec 2023 13:00:49 +0000Geometries and Groups
https://resolver.caltech.edu/CaltechAUTHORS:20190814-100149802
Authors: Aschbacher, M.; Cohen, A. M.; Kantor, W. M.
Year: 1987
DOI: 10.1007/978-94-009-4017-8
The workshop was set up in order to stimulate the interaction between (finite and algebraic) geometries and groups. Five areas of concentrated research were chosen on which attention would be focused, namely: diagram geometries and chamber systems with transitive automorphism groups, geometries viewed as incidence systems, properties of finite groups of Lie type, geometries related to finite simple groups, and algebraic groups. The list of talks (cf. page iii) illustrates how these subjects were represented during the workshop. The contributions to these proceedings mainly belong to the first three areas; therefore, (i) diagram geometries and chamber systems with transitive automorphism groups, (ii) geometries viewed as incidence systems, and (iii) properties of finite groups of Lie type occur as section titles. The fourth and final section of these proceedings has been named graphs and groups; besides some graph theory, this encapsules most of the work related to finite simple groups that does not (explicitly) deal with diagram geometry. A few more words about the content: (i). Diagram geometries and chamber systems with transitive automorphism groups. As a consequence of Tits' seminal work on the subject, all finite buildings are known. But usually, in a situation where groups are to be characterized by certain data concerning subgroups, a lot less is known than the full parabolic picture corresponding to the building.https://authors.library.caltech.edu/records/my4ef-an845Fusion Systems in Algebra and Topology
https://resolver.caltech.edu/CaltechAUTHORS:20180807-124803752
Authors: Aschbacher, Michael; Kessar, Radha; Oliver, Bob
Year: 2011
DOI: 10.1017/CBO9781139003841
A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.https://authors.library.caltech.edu/records/r5359-bqa87Overgroups of Root Groups in Classical Groups
https://resolver.caltech.edu/CaltechAUTHORS:20160425-141046633
Authors: Aschbacher, Michael
Year: 2016
DOI: 10.1090/memo/1140
We extend results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular we determine the maximal subgroups of this form. We also determine the maximal overgroups of short root subgroups in finite classical groups, and the maximal overgroups in finite orthogonal groups of c-root subgroups.https://authors.library.caltech.edu/records/yzaqr-6fd02