Michael Aschbacher | Academic Influence

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Michael Aschbacher

Mathematics

#772

World Rank

#1397

Historical Rank

#337

USA Rank

Measure Theory

#1294

World Rank

#1636

Historical Rank

#466

USA Rank

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Mathematics

Michael Aschbacher's Degrees

Bachelors Mathematics University of California, Berkeley

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Why Is Michael Aschbacher Influential?

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According to Wikipedia, Michael George Aschbacher is an American mathematician best known for his work on finite groups. He was a leading figure in the completion of the classification of finite simple groups in the 1970s and 1980s. It later turned out that the classification was incomplete, because the case of quasithin groups had not been finished. This gap was fixed by Aschbacher and Stephen D. Smith in 2004, in a pair of books comprising about 1300 pages. Aschbacher is currently the Shaler Arthur Hanisch Professor of Mathematics at the California Institute of Technology.

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Michael Aschbacher's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

On the maximal subgroups of the finite classical groups (1984) (612)
Corrections to “Involutions in Chevalley groups over fields of even order” (1976) (275)
Fusion Systems in Algebra and Topology (2011) (247)
Finite Group Theory (1994) (243)
Some applications of the first cohomology group (1984) (202)
Finite Group Theory: Index (2000) (179)
A Characterization of Chevalley Groups Over Fields of Odd Order (1977) (129)
Maximal subgroups of finite groups (1985) (104)
Chevalley groups of type G2 as the group of a trilinear form (1987) (100)
On finite groups of component type (1975) (95)
The Status of the Classification of the Finite Simple Groups (2004) (74)
Flag structures on tits geometries (1983) (73)
The 27-dimensional module forE6. I (1987) (73)
Involutions in Chevalley groups over fields of even order (1976) (72)
Sporadic groups (1994) (66)
The Generalized Fitting Subsystem of a Fusion System (2011) (66)
On Collineation Groups of Symmetric Block Designs (1971) (65)
On groups with a standard component of known type. II (1981) (63)
On finite groups generated by odd transpositions. I (1972) (62)
Finite Group Theory: p -groups (2000) (60)
Overgroups of Sylow subgroups in sporadic groups (1986) (56)
The 27-dimensional module for E6, IV (1990) (54)
Some multilinear forms with large isometry groups (1988) (54)
ON ABELIAN QUOTIENTS OF PRIMITIVE GROUPS (1989) (53)
The nonexistence of rank three permutation groups of degree 3250 and subdegree 57 (1971) (53)
On Quillen’s conjecture for the $p$-groups complex (1993) (51)
The limitations of nice mutually unbiased bases (2004) (50)
The Classification of Quasithin Groups (2004) (47)
Groups Generated by a Class of Elements of Order 3. (1973) (44)
Simple connectivity ofp-group complexes (1993) (43)
Near subgroups of finite groups (1998) (43)
Finite groups with a proper 2-generated core (1974) (41)
Finite Group Theory: Representations of groups on groups (2000) (37)
Solvable generation of groups and Sylow subgroups of the lower central series (1982) (36)
On finite groups of Lie type and odd characteristic (1980) (36)
Tits geometries over gf(2) Defined by groups over gf(3) (1983) (35)
3-transposition groups (1997) (33)
On Bol loops of exponent 2 (2005) (33)
Thin finite simple groups (1976) (32)
The finite simple groups and their classification (1980) (32)
On intervals in subgroup lattices of finite groups (2008) (31)
Finite geometries of type C3 with flag-transitive groups (1984) (30)
The 27‐Dimensional Module for E6, II (1988) (29)
A condition for the existence of a strongly embedded subgroup (1973) (29)
Review: Peter Kleidman and Martin Liebeck, The subgroup structure of the finite classical groups (1991) (28)
On conjectures of Guralnick and Thompson (1990) (28)
FUSION SYSTEMS (2016) (27)
GF(2)-Representations of Finite Groups (1982) (26)
Generation of fusion systems of characteristic 2-type (2010) (25)
On finite groups in which the generalized fitting group of the centralizer of some involution is extraspecial (1977) (25)
Normal subsystems of fusion systems (2008) (25)
Highly complex proofs and implications of such proofs (2005) (24)
Doubly transitive groups in which the stabilizer of two points is Abelian (1971) (24)
A homomorphism theorem for finite graphs (1976) (24)
The Classification of the Finite Simple Groups (1980) (23)
Finite Bruck loops (2004) (23)
The Classification of Finite Simple Groups: Groups of Characteristic 2 Type (2011) (22)
Tightly embedded subgroups of finite groups (1976) (21)
Extending morphisms of groups and graphs (1992) (21)
A group-theoretic approach to a family of $2$-local finite groups constructed by Levi and Oliver (2010) (21)
Main theorems : the classification of simple QTKE-groups (2004) (21)
A Factorization Theorem for 2‐Constrained Groups (1981) (20)
T-sets and permutation groups (1974) (19)
On finite groups generated by odd transpositions, III (1973) (17)
Embeddings of ultrametric spaces in finite dimensional structures (1987) (17)
The uniqueness of groups of Lyons type (1992) (16)
OVERGROUPS OF PRIMITIVE GROUPS (2009) (15)
On a conjecture of Quillen and a lemma of Robinson (1990) (15)
Finite groups in which the generalized fitting group of the centraliser of some involution is symplectic but not extraspecial (1976) (14)
The 27-dimensional module for ₆. III (1990) (14)
A Fixed Point Theorem for Groups Acting on Finite 2‐Dimensional Acyclic Simplicial Complexes (1993) (13)
On doubly transitive permutation groups of degree $n \equiv 2$ mod $4$ (1972) (13)
A characterization of the unitary and symplectic groups over finite fields of characteristic at least $5$ (1973) (13)
A characterization of certain Frobenius groups (1974) (12)
A CHARACTERIZATION OF CERTAIN CHEVALLEY GROUPS AND ITS APPLICATION TO COMPONENT TYPE GROUPS (1976) (12)
On Fusion Systems of Component Type (2018) (11)
Proceedings of the Rutgers Group Theory Year, 1983-1984 (2008) (11)
On the Failure of the Thompson Factorization in 2-Constrained Groups (1981) (11)
Signalizer lattices in finite groups (2009) (11)
Restrictions on the structure of subgroup lattices of finite alternating and symmetric groups (2009) (11)
The Uniqueness Case for Finite Groups (1983) (10)
S3-free 2-fusion systems (2012) (10)
A pushing up theorem for characteristic $2$ type groups (1978) (10)
The existence of J3 and its embeddings in E6 (1990) (9)
Overgroups of primitive groups, II (2009) (9)
2-transitive groups whose 2-point stabilizer has 2-rank 1 (1975) (9)
Quaternion Fusion Packets (2021) (9)
Locally connected simplicial maps (1992) (9)
The embedding of 2-locals in finite groups of characteristic 2-type, II (1981) (9)
Finite groups of rank 3. I (1981) (8)
A class of generalized $TI$-groups (1972) (8)
Finite simple groups and their subgroups (1986) (8)
Correction to "A Characterization of Chevalley Groups over Fields of Odd Order" (1980) (8)
Classifying Finite Simple Groups and 2-Fusion Systems (2015) (8)
Some results on pushing up in finite groups (1981) (7)
A 2-local characterization of M(12) (2003) (7)
Combinatorial Cell Complexes (1996) (6)
On Finite Groups Generated by Odd Transpositions, IV (2003) (6)
A 2-local characterization of the Higman–Sims group (2003) (6)
Overgroup lattices in finite groups of Lie type containing a parabolic (2013) (6)
2-Components in finite groups (1975) (6)
Weak closure in finite groups of even characteristic (1981) (6)
Groups of Lie Type and their Geometries: Representations of groups on finite simplicial complexes (1995) (5)
On Primitive Linear Representations of Finite Groups (2000) (5)
The uniqueness of groups of typeJ4 (1991) (5)
Standard components of alternating type centralized by a 4-group (2008) (5)
Projective planes, loops, and groups (2006) (4)
Walter's theorem for fusion systems (2020) (4)
Fusion systems of F_2-type (2013) (4)
The subgroup structure of finite groups (2017) (4)
Finite groups of G2(3)-type (2002) (3)
Lower signalizer lattices in alternating and symmetric groups (2012) (3)
The tits group as a standard subgroup (1982) (2)
FINITE GROUPS ACTING ON HOMOLOGY MANIFOLDS (1997) (2)
Structure of strongly quasithin Κ-groups (2004) (2)
THE SUBGROUP STRUCTURE OF FINITE ALTERNATING AND SYMMETRIC GROUPS (2008) (2)
Exponents of almost simple groups and an application to the restricted Burnside problem (1991) (2)
N-groups and fusion systems (2016) (2)
Finite Simple Groups and Fusion Systems (2019) (2)
Isotopy and geotopy for ternary rings of projective planes (2008) (2)
The 2-fusion system of an almost simple group (2020) (2)
Fusion Systems in Algebra and Topology: Fusion and Representation theory (2011) (2)
Overgroups of Root Groups in Classical Groups (2016) (1)
Quanternion Fusion Packets (2021) (1)
An introduction to the classification of finite simple groups (1979) (1)
Finite Group Theory: Preface (2000) (1)
Fusion systems with alternating J‐components (2020) (1)
A characterization of some finite groups of characteristic 3 (1982) (1)
Groups, Combinatorics & Geometry: Uniqueness of sporadic groups (1992) (1)
Finite Group Theory: Presentations of groups (2000) (1)
Finite Groups of Seitz Type (2013) (1)
Mathematicians and Mathematics (2015) (1)
Elementary abelian 2-subgroups of Sidki-type in finite groups (2007) (1)
Finite Groups Generated by Odd Transpositions (1973) (1)
Finite groups of rank 3. II (1983) (1)
Walter's basic theorem for fusion systems (2020) (1)
Eliminating shadows and characterizing the ₄ example (2004) (0)
Generation and weak closure (2004) (0)
Background facts about groups (2011) (0)
Fusion systems with J-components over 𝐹2𝑒 with 𝑒 > 1 (2022) (0)
Mid-size groups over ₂ (2004) (0)
Sporadic groups: The Griess Algebra and the Monster (1994) (0)
Fusion and homotopy theory (2011) (0)
Various representation-theoretic lemmas (2004) (0)
The case ∈ℒ*_{}(,) not normal in ℳ (2004) (0)
()≤2: The classification of quasithin groups (2011) (0)
Sporadic groups: The Geometry and Structure of M24 (1994) (0)
3-Transposition groups: Fischer's Theorem (1996) (0)
FINITE GROUPS OF SEITZ TYPE 115 Lemma (2013) (0)
Overview: The classification of groups of Gorenstein-Walter type (2011) (0)
Sporadic groups: Subgroups of ·0 (1994) (0)
Sporadic groups: The Mathieu Groups, Their Steiner Systems, and the Golay Code (1994) (0)
Groups, Combinatorics & Geometry: The study of J4 via the theory of uniqueness systems (1992) (0)
Fusion Systems in Algebra and Topology: Introduction (2011) (0)
Determining the cases for ∈ℒ*_{}(,) (2004) (0)
Fusion systems with U3(3) J-components (2021) (0)
Fusion Systems in Algebra and Topology: References (2011) (0)
Pushing up in QTKE-groups (2004) (0)
Quasithin groups of even type but not even characteristic (2004) (0)
Sporadic groups: Preface (1994) (0)
Geometries and Groups (2011) (0)
Titles and abstracts for Fusion Systems and Finite Simple Groups Workshop (2014) (0)
3-Transposition groups: The structure of 3-transposition groups (1996) (0)
Sporadic groups: The Conway Groups and the Leech Lattice (1994) (0)
Abstracts of lectures for Banff meeting , Groups and Geometries , May 4-8 , 2015 (2015) (0)
3-Transposition groups: Index (1996) (0)
Sporadic groups: The Uniqueness of Groups of Type M24, He , and L 5(2) (1994) (0)
Selected Mathematical Reviews Related to the Paper in the Previous Section By (0)
Finite Group Theory: Transfer and fusion (2000) (0)
Finite Group Theory: Permutation groups (2000) (0)
Sporadic groups: Preliminary Results (1994) (0)
Sporadic groups: Subgroups of Groups of Monster Type (1994) (0)
What is the Case? (2004) (0)
3-Transposition groups: Some group extensions (1996) (0)
₃(2) in the FSU, and ₂(2) when ℒ_{}(,) is empty (2004) (0)
Walter's theorem for fusion systems (2021) (0)
3-Transposition groups: Preliminaries (1996) (0)
3-Transposition groups: Almost 3-transposition groups (1996) (0)
Finite Group Theory: Appendix (2000) (0)
Basic results related to failure of factorization (2004) (0)
Fusion Systems in Algebra and Topology: The local theory of fusion systems (2011) (0)
Book Review: The classification of the finite simple groups (1995) (0)
Finite Group Theory: Permutation representations (2000) (0)
Sporadic groups: 2-Structure in Finite Groups (1994) (0)
A characterization of the Rudvalis group (2004) (0)
3-Transposition groups: Uniqueness systems and coverings of graphs (1996) (0)
Sporadic groups: The Discovery, Existence, and Uniqueness of the Sporadics (1994) (0)
Finite Group Theory: Linear representations (2000) (0)
Overview of some techniques used in the classification (2011) (0)
3-Transposition groups: Odd locals in Fischer groups (1996) (0)
Finite Group Theory: Extensions of groups and modules (2000) (0)
3-Transposition groups: The existence and uniqueness of the Fischer groups (1996) (0)
Some background material related to simple groups (2011) (0)
The -lemma and modules with ≤2 (2004) (0)
A CHARACTERIZATION OF CERTAIN FROBENlUS GROUPS (0)
Sporadic groups: Groups of Conway, Suzuki, and Hall–Janko Type (1994) (0)
()≥4: The pretrichotomy and trichotomy theorems (2011) (0)
Overview: The classification of groups of characteristic 2 type (2011) (0)
3-Transposition groups: Commuting graphs of groups (1996) (0)
Statements of some quoted results (2004) (0)
Daniel Gorenstein, 1923-1992 - A Biographical Memoir byMichael Aschbacher (2016) (0)
Sporadic groups: Algebras, Codes, and Forms (1994) (0)
The classification of groups of (2) type (2011) (0)
Sporadic groups: Bibliography (1994) (0)
Finite Group Theory: The geometry of groups of Lie type (2000) (0)
Finite Group Theory: Finite simple groups (2000) (0)
Parameters for some modules (2004) (0)
Linear representations of finite groups (2000) (0)
Sporadic groups: Symplectic 2-Loops (1994) (0)
Finite Group Theory: Preliminary results (2000) (0)
Larger groups over ₂ in ℒ*_{}(,) (2004) (0)
Modules for SQTK-groups with (,)≤2 (2004) (0)
The final contradiction: Eliminating the Uniqueness Case (2011) (0)
Classifying the groups with |ℳ()|=1 (2004) (0)
Olga Taussky-Todd : in memoriam : a special issue of the Pacific Journal of Mathematics (1988) (0)
Structure and intersection properties of 2-locals (2004) (0)
Finite Group Theory: Signalizer functors (2000) (0)
3-Transposition groups: References (1996) (0)
3-Transposition groups: Classical groups generated by 3-transpositions (1996) (0)
Reducing ₂(2ⁿ) to =2 and V orthogonal (2004) (0)
Eliminating cases corresponding to no shadow (2004) (0)
Fusion Systems in Algebra and Topology: Introduction to fusion systems (2011) (0)
Geometries and groups : proceedings of the Workshop Geometries and Groups, Finite and Algebraic, Noordwijkerhout, Holland, March 1986 (1988) (0)
Weak BN-pairs and amalgams (2004) (0)
Finite Group Theory: Spaces with forms (2000) (0)
Elementary group theory and the known quasithin groups (2004) (0)
3-Transposition groups: Introduction (1996) (0)
Finite Group Theory: Change of field of a linear representation (2000) (0)
3-Transposition groups: The 2-local structure of the Fischer groups (1996) (0)
Finite Group Theory: The generalized Fitting subgroup (2000) (0)
Sporadic groups: The Group U 4(3) (1994) (0)
Michio Suzuki (1926–1998), Volume 46, Number 5 (1999) (0)
A characterization of ${}^2\mathrm{E}_6(2)$ (2001) (0)
Sporadic groups: Subgroups of Prime Order in Five Sporadic Groups (1994) (0)
3-Transposition groups: Elements of order 3 in orthogonal groups over GF(3) (1996) (0)
3-Transposition groups: U 4(3) as a subgroup of U 6(2) (1996) (0)
3-Transposition groups: The geometry of 3-transposition groups (1996) (0)
3-Transposition groups: Normalizers of subgroups of prime order in Fischer groups (1996) (0)
04 12 06 6 v 1 8 D ec 2 00 4 The limitations of nice mutually unbiased bases (2018) (0)
Elimination of ₃(2ⁿ), ₄(2ⁿ), and ₂(2ⁿ) for >1 (2004) (0)
The generic case: ₂(2ⁿ) in ℒ_{} and (ℋ)>1 (2004) (0)
Finite Group Theory: References (2000) (0)
Michael Aschbacher proofs Highly complex proofs and implications of such (2008) (0)
Eliminating Ω⁺₄(2ⁿ) on its orthogonal module (2004) (0)
Sporadic groups: The Geometry of Amalgams (1994) (0)
Sporadic groups: Coverings of Graphs and Simplicial Complexes (1994) (0)
The classification of groups of standard type (2011) (0)
COUNTING INVOLUTIONS (2003) (0)
()=3: The classification of rank 3 groups (2011) (0)
Finite Groups Acting on Homology Manifolds Michael Aschbacher (1997) (0)

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