Aschbacher, Michael 1944
Overview
Works:  57 works in 291 publications in 1 language and 4,692 library holdings 

Genres:  Conference papers and proceedings Classification 
Roles:  Author, Editor, Other, Thesis advisor 
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
)
43 editions published between 1986 and 2000 in English and Undetermined and held by 926 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
43 editions published between 1986 and 2000 in English and Undetermined and held by 926 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
Fusion systems in algebra and topology by
Michael Aschbacher(
)
14 editions published in 2011 in English and held by 631 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 631 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."
Sporadic groups by
Michael Aschbacher(
Book
)
18 editions published between 1994 and 2008 in English and Undetermined and held by 433 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
18 editions published between 1994 and 2008 in English and Undetermined and held by 433 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
)
13 editions published in 1980 in English and held by 364 WorldCat member libraries worldwide
13 editions published in 1980 in English and held by 364 WorldCat member libraries worldwide
3transposition groups by
Michael Aschbacher(
Book
)
15 editions published between 1997 and 2009 in English and Undetermined and held by 337 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
15 editions published between 1997 and 2009 in English and Undetermined and held by 337 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
)
11 editions published between 1984 and 2008 in English and held by 315 WorldCat member libraries worldwide
11 editions published between 1984 and 2008 in English and held by 315 WorldCat member libraries worldwide
The classification of quasithin groups by
Michael Aschbacher(
Book
)
22 editions published between 2004 and 2014 in English and held by 306 WorldCat member libraries worldwide
This is the second volume of a twovolume set, which take up where Geoff Mason left off in the 1980x on the issue of quasithin groups of even characteristics. V.2 gives the proof that the groups listed in the Main Theorem are the simple quasithin groups of even characteristicsall of whose proper simple sections are known simple groups. This lively and comprehensive proof includes the structure of QTKEgroups and the main case division, treatments of the generic case and modules which are not FFmodules, and certain pairs in the FSU. While the two volumes address one issue of mathematics, they also serve as models of presentation for analyses Annotation : 2004 Book News, Inc., Portland, OR (booknews.com)
22 editions published between 2004 and 2014 in English and held by 306 WorldCat member libraries worldwide
This is the second volume of a twovolume set, which take up where Geoff Mason left off in the 1980x on the issue of quasithin groups of even characteristics. V.2 gives the proof that the groups listed in the Main Theorem are the simple quasithin groups of even characteristicsall of whose proper simple sections are known simple groups. This lively and comprehensive proof includes the structure of QTKEgroups and the main case division, treatments of the generic case and modules which are not FFmodules, and certain pairs in the FSU. While the two volumes address one issue of mathematics, they also serve as models of presentation for analyses Annotation : 2004 Book News, Inc., Portland, OR (booknews.com)
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 268 WorldCat member libraries worldwide
The book provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the ""even case"", where the main groups arising are Lietype (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of ""noncharacteristic 2 type"". However, this book provides much more. Chapter 0 is a modern overview of the logical structure of the entire classification. Chapter 1 is a concise but complete outline of the ""odd case"" with updated references, whi
11 editions published in 2011 in English and held by 268 WorldCat member libraries worldwide
The book provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the ""even case"", where the main groups arising are Lietype (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of ""noncharacteristic 2 type"". However, this book provides much more. Chapter 0 is a modern overview of the logical structure of the entire classification. Chapter 1 is a concise but complete outline of the ""odd case"" with updated references, whi
Overgroups of Sylow subgroups in sporadic groups by
Michael Aschbacher(
Book
)
10 editions published in 1986 in English and held by 247 WorldCat member libraries worldwide
10 editions published in 1986 in English and held by 247 WorldCat member libraries worldwide
The generalized fitting subsystem of a fusion system by
Michael Aschbacher(
Book
)
16 editions published between 2010 and 2011 in English and held by 230 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."
16 editions published between 2010 and 2011 in English and held by 230 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."
Geometries and groups : proceedings of the Workshop Geometries and Groups, Finite and Algebraic, Noordwijkerhout, Holland,
March 1986 by
Michael Aschbacher(
Book
)
13 editions published between 1987 and 1988 in English and held by 169 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
13 editions published between 1987 and 1988 in English and held by 169 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
)
12 editions published between 2015 and 2016 in English and held by 139 WorldCat member libraries worldwide
The author extends results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular he determines the maximal subgroups of this form. He also determines the maximal overgroups of short root subgroups in finite classical groups and the maximal overgroups in finite orthogonal groups of croot subgroups
12 editions published between 2015 and 2016 in English and held by 139 WorldCat member libraries worldwide
The author extends results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular he determines the maximal subgroups of this form. He also determines the maximal overgroups of short root subgroups in finite classical groups and the maximal overgroups in finite orthogonal groups of croot subgroups
Olga TausskyTodd : in memoriam : a special issue of the Pacific journal of mathematics by
Michael Aschbacher(
Book
)
16 editions published between 1988 and 1998 in English and Undetermined and held by 112 WorldCat member libraries worldwide
16 editions published between 1988 and 1998 in English and Undetermined and held by 112 WorldCat member libraries worldwide
The classification of quasithin groups. the classification of simple QTKEgroups by
Michael Aschbacher(
Book
)
15 editions published between 2004 and 2014 in English and held by 58 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
15 editions published between 2004 and 2014 in English and held by 58 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
Sporadic Groups by
Michael Aschbacher(
)
3 editions published in 1994 in English and held by 24 WorldCat member libraries worldwide
3 editions published in 1994 in English and held by 24 WorldCat member libraries worldwide
3Transposition Groups by
Michael Aschbacher(
)
2 editions published in 1996 in English and held by 21 WorldCat member libraries worldwide
2 editions published in 1996 in English and held by 21 WorldCat member libraries worldwide
Overgroups of Sylow subgroups in sporadic groups by
Michael Aschbacher(
Book
)
3 editions published in 1986 in English and held by 17 WorldCat member libraries worldwide
3 editions published in 1986 in English and held by 17 WorldCat member libraries worldwide
Finite group theory by
Michael Aschbacher(
Book
)
7 editions published between 1986 and 2000 in English and held by 13 WorldCat member libraries worldwide
7 editions published between 1986 and 2000 in English and held by 13 WorldCat member libraries worldwide
Structure of strongly quasithin kgroups by
Michael Aschbacher(
Book
)
1 edition published in 2004 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 7 WorldCat member libraries worldwide
Main theorems the classification of simple QTKEgroups by
Michael Aschbacher(
Book
)
1 edition published in 2004 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 7 WorldCat member libraries worldwide
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Related Identities
 Oliver, Robert 1949
 Kessar, Radha
 Smith, Stephen D. 1948 Other
 Kantor, W. M. (William M.) 1944 Other Editor
 Cohen, Arjeh M. Other Editor
 Taussky, Olga Honoree Editor
 Blasius, Don Editor
 Ramakrishnan, Dinakar Editor
 American Mathematical Society
 Smith, Stephen D. Other
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Associated Subjects
Algebra Algebraic topology Canada College teachers Combinatorial group theory Educational assistance 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
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Alternative Names
Aschbacher, M.
Aschbacher, M. 1944
Aschbacher, M. (Michael), 1944
Aschbacher, Michael.
Aschbacher, Michael George
Michael Aschbacher American mathematician
Michael Aschbacher Amerikaans wiskundige
Michael Aschbacher amerikansk matematikar
Michael Aschbacher amerikansk matematiker
Michael Aschbacher matemático estadounidense
Michael Aschbacher matematico statunitense
Michael Aschbacher mathématicien américain
Michael Aschbacher USamerikanischer Mathematiker
Μάικλ Ασμπάχερ
Майкл Ашбахер американский математик
מייקל אשבכר מתמטיקאי אמריקאי
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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