WorldCat Identities

Aschbacher, Michael 1944-

Overview
Works: 58 works in 271 publications in 1 language and 4,126 library holdings
Genres: Conference papers and proceedings  Classification 
Roles: Author, Editor, Other, Thesis advisor
Classifications: QA177, 512.2
Publication Timeline
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Most widely held works about Michael Aschbacher
 
Most widely held works by Michael Aschbacher
Finite group theory by Michael Aschbacher( Book )

44 editions published between 1986 and 2000 in English and Undetermined and held by 890 WorldCat member libraries worldwide

This work develops the foundations of the theory of finite groups. It can serve as a text for a course on finite groups for students already exposed to a first course in algebra
Sporadic groups by Michael Aschbacher( Book )

19 editions published between 1994 and 2008 in English and Undetermined and held by 419 WorldCat member libraries worldwide

The Monster is constructed as the automorphism group of the Griess algebra using some of the best features of the approaches of Griess, Conway, and Tits, plus a few new wrinkles. The existence treatment finishes with an application of the theory of large extraspecial subgroups to produce the 20 sporadics involved in the Monster
The finite simple groups and their classification by Michael Aschbacher( Book )

11 editions published in 1980 in English and held by 361 WorldCat member libraries worldwide

3-transposition groups by Michael Aschbacher( Book )

17 editions published between 1996 and 2009 in English and Undetermined and held by 326 WorldCat member libraries worldwide

Parts II and III are aimed at specialists in finite groups. They establish the existence, uniqueness, and structural results for the Fischer groups, necessary for the classification of the finite simple groups. Parts II and III are a step in the author's program (begun in Sporadic Groups) to supply a strong foundation for the theory of sporadic groups
Proceedings of the Rutgers group theory year, 1983-1984 by New Brunswick, NJ) Rutgers Group Theory Year (1983 - 1984( Book )

10 editions published between 1984 and 2008 in English and held by 313 WorldCat member libraries worldwide

The classification of quasithin groups by Michael Aschbacher( Book )

19 editions published in 2004 in English and held by 273 WorldCat member libraries worldwide

In around 1980, G. Mason announced the classification of a subclass of an important class of finite simple groups known as 'quasithin groups'. In the main theorem of this two-part work the authors provide a proof of a stronger theorem classifying a larger class of groups independently of Mason's research
The classification of finite simple groups : groups of characteristic 2 type by Michael Aschbacher( Book )

11 editions published in 2011 in English and held by 232 WorldCat member libraries worldwide

Overgroups of Sylow subgroups in sporadic groups by Michael Aschbacher( Book )

10 editions published in 1986 in English and held by 224 WorldCat member libraries worldwide

Fusion systems in algebra and topology by Michael Aschbacher( Book )

14 editions published in 2011 in English and held by 216 WorldCat member libraries worldwide

"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. The book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians"--
The generalized fitting subsystem of a fusion system by Michael Aschbacher( Book )

13 editions published between 1900 and 2011 in English and held by 152 WorldCat member libraries worldwide

"The notion of a fusion system was first defined and explored by Puig, in the context of modular representation theory. Later, Broto, Levi, and Oliver extended the theory and used it as a tool in homotopy theory. We seek to build a local theory of fusion systems, analogous to the local theory of finite groups, involving normal subsystems and factor systems. Among other results, we define the notion of a simple system, the generalized Fitting subsystem of a fusion system, and prove the L-balance theorem of Gorenstein and Walter for fusion systems. We define a notion of composition series and composition factors, and prove a Jordon-Hölder theorem for fusion systems."
Olga Taussky-Todd : in memoriam : a special issue of the Pacific journal of mathematics by Michael Aschbacher( Book )

14 editions published between 1988 and 1998 in English and Undetermined and held by 103 WorldCat member libraries worldwide

Geometries and groups : proceedings of the Workshop Geometries and Groups, Finite and Algebraic, Noordwijkerhout, Holland, March 1986 by Michael Aschbacher( Book )

11 editions published between 1987 and 1988 in English and held by 101 WorldCat member libraries worldwide

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
Overgroups of root groups in classical groups by Michael Aschbacher( Book )

7 editions published in 2016 in English and held by 65 WorldCat member libraries worldwide

The classification of quasithin groups by Michael Aschbacher( Book )

8 editions published in 2004 in English and held by 26 WorldCat member libraries worldwide

The generalized fitting subsystem of a fusion system by Michael Aschbacher( Book )

3 editions published in 2011 in English and held by 17 WorldCat member libraries worldwide

The classification of quasithin groups. Structure of strongly quasithin k-groups by Michael Aschbacher( Book )

9 editions published between 2004 and 2005 in English and held by 8 WorldCat member libraries worldwide

The first of two volumes, this text offers results that are used in the proof of the main theoremthat lies behind quasithin groups, an class of finite simple groups. Some results are gathered from existing mathematical literature, but many are proven for the first time
Main theorems the classification of simple QTKE-groups by Michael Aschbacher( Book )

2 editions published in 2004 in English and held by 8 WorldCat member libraries worldwide

Collineation groups of symmetric block designs by Michael Aschbacher( )

3 editions published in 1969 in English and held by 4 WorldCat member libraries worldwide

Overgroup of sylow subgroups in sporadic groups by Michael Aschbacher( Book )

1 edition published in 1986 in English and held by 4 WorldCat member libraries worldwide

Overgroups of sylow subgroups in sporadic groups by Michael Aschbacher( )

1 edition published in 1986 in English and held by 0 WorldCat member libraries worldwide

 
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Sporadic groups
Alternative Names
Aschbacher, M.

Aschbacher, M. 1944-

Aschbacher, M. (Michael), 1944-

Aschbacher, Michael.

Michael Aschbacher Amerikaans wiskundige

Michael Aschbacher amerikansk matematikar

Michael Aschbacher amerikansk matematiker

Michael Aschbacher matematico statunitense

Michael Aschbacher mathématicien américain

Michael Aschbacher US-amerikanischer Mathematiker

Μάικλ Ασμπάχερ

Майкл Ашбахер американский математик

מיכאל אשבכר

ミハエル・アッシュバッハー

邁克爾·阿什巴赫

麥克·阿什巴赫

Languages
English (221)

Covers
Sporadic groups3-transposition groupsProceedings of the Rutgers group theory year, 1983-1984The classification of quasithin groupsThe classification of finite simple groups : groups of characteristic 2 typeFusion systems in algebra and topologyThe generalized fitting subsystem of a fusion systemGeometries and groups : proceedings of the Workshop Geometries and Groups, Finite and Algebraic, Noordwijkerhout, Holland, March 1986