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Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type

2020-02-13 Education
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Release : 2020-02-13
Genre : Education
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Book Rating : 724/5 ( reviews)

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Book Synopsis Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type by : Carles Broto

Download or read book Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type written by Carles Broto. This book was released on 2020-02-13. Available in PDF, EPUB and Kindle. Book excerpt: For a finite group G of Lie type and a prime p, the authors compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic, with a very short list of exceptions. When p is different from the defining characteristic, the situation is much more complex but can always be reduced to a case where the natural map from Out(G) to outer automorphisms of the fusion or linking system is split surjective. This work is motivated in part by questions involving extending the local structure of a group by a group of automorphisms, and in part by wanting to describe self homotopy equivalences of BG∧p in terms of Out(G).

Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type

2019 Finite simple groups
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Release : 2019
Genre : Finite simple groups
Kind : eBook
Book Rating : 071/5 ( reviews)

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Book Synopsis Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type by : Carles Broto

Download or read book Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type written by Carles Broto. This book was released on 2019. Available in PDF, EPUB and Kindle. Book excerpt: For a finite group G of Lie type and a prime p, we compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic, with a very short list of exceptions. When p is different from the defining characteristic, the situation is much more complex, but can always be reduced to a case where the natural map from Out(G) to outer automorphisms of the fusion or linking system is split surjective. This work is motivated in part by questions involving extending the local structure of a group by a group of automorphisms, and in part by wanting to describe self homotopy equivalences of the p-completion of the classifying space BG in terms of Out(G).

Rank 2 Amalgams and Fusion Systems

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Book Rating : 617/5 ( reviews)

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Book Synopsis Rank 2 Amalgams and Fusion Systems by : Martin van Beek

Download or read book Rank 2 Amalgams and Fusion Systems written by Martin van Beek. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:

Geometric and Topological Aspects of the Representation Theory of Finite Groups

2018-10-04 Mathematics
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Release : 2018-10-04
Genre : Mathematics
Kind : eBook
Book Rating : 333/5 ( reviews)

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Book Synopsis Geometric and Topological Aspects of the Representation Theory of Finite Groups by : Jon F. Carlson

Download or read book Geometric and Topological Aspects of the Representation Theory of Finite Groups written by Jon F. Carlson. This book was released on 2018-10-04. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.

Fusion Systems in Algebra and Topology

2011-08-25 Mathematics
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Release : 2011-08-25
Genre : Mathematics
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Book Rating : 002/5 ( reviews)

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Book Synopsis Fusion Systems in Algebra and Topology by : Michael Aschbacher

Download or read book Fusion Systems in Algebra and Topology written by Michael Aschbacher. This book was released on 2011-08-25. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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