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
 Finite Simple Group Theory, collection by Joseph A Gallian( )
 Aschbacher, Michael : Finite Group Theory( )
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
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
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
11 editions published in 1980 in English and held by 361 WorldCat member libraries worldwide
3transposition 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
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, 19831984 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
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 twopart work the authors provide a proof of a stronger theorem classifying a larger class of groups independently of Mason's research
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 twopart 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
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
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 pgroup 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 pcompleted 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"
14 editions published in 2011 in English and held by 216 WorldCat member libraries worldwide
"A fusion system over a pgroup 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 pcompleted 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 Lbalance theorem of Gorenstein and Walter for fusion systems. We define a notion of composition series and composition factors, and prove a JordonHölder theorem for fusion systems."
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 Lbalance theorem of Gorenstein and Walter for fusion systems. We define a notion of composition series and composition factors, and prove a JordonHölder theorem for fusion systems."
Olga TausskyTodd : 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
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
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
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
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
3 editions published in 2011 in English and held by 17 WorldCat member libraries worldwide
The classification of quasithin groups. Structure of strongly quasithin kgroups 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
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 QTKEgroups by
Michael Aschbacher(
Book
)
2 editions published in 2004 in English and held by 8 WorldCat member libraries worldwide
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
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
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
1 edition published in 1986 in English and held by 0 WorldCat member libraries worldwide
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Related Identities
 Smith, Stephen D. 1948
 Oliver, Robert 1949
 Kessar, Radha
 Kantor, W. M. (William M.) 1944 Other Editor
 Cohen, Arjeh M. Other Editor
 Blasius, Don Editor
 Taussky, Olga Honoree Editor
 Ramakrishnan, Dinakar Editor
 Taussky, Olga
 American Mathematical Society
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Associated Subjects
Algebra Algebraic topology Canada College teachers Collineation Combinatorial group theory Educational assistance Experimental design Finite groups Finite simple groups Geometry Glauberman, G., Group theory Mathematicians Mathematics Number theory Representations of groups Scientists Sporadic groups (Mathematics) Sylow subgroups Taussky, Olga Topological groups United States
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 USamerikanischer 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
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