Gary Seitz
American mathematician
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Mathematics
Gary Seitz's Degrees
- PhD Mathematics University of California, Berkeley
- Bachelors Mathematics University of California, Berkeley
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Why Is Gary Seitz Influential?
(Suggest an Edit or Addition)According to Wikipedia, Gary Michael Seitz is an American mathematician, a Fellow of the American Mathematical Society and a College of Arts and Sciences Distinguished Professor Emeritus in Mathematics at the University of Oregon. He received his Ph.D. from the University of Oregon in 1968, where his adviser was Charles W. Curtis. Seitz specializes in the study of algebraic and finite groups. Seitz has been active in the effort to exploit the relationship between algebraic groups and the finite groups of Lie type, in order to study the structure and representations of groups in the latter class. Such information is important in its own right, but was also critical in the classification of the finite simple groups, a major achievement of 20th century mathematics. Seitz made contributions to the classification of finite simple groups, such as those containing standard subgroups of Lie type. Following the classification, he pioneered the study of the subgroup structure of simple algebraic groups, and as an application went a long way towards solving the maximal subgroup problem for finite groups. For this work he received the Creativity Award from the National Science Foundation in 1991.
Gary Seitz's Published Works
Published Works
- On the minimal degrees of projective representations of the finite Chevalley groups (1974) (404)
- Corrections to “Involutions in Chevalley groups over fields of even order” (1976) (275)
- SUBGROUPS OF MAXIMAL RANK IN FINITE EXCEPTIONAL GROUPS OF LIE TYPE (1992) (207)
- Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras (2012) (205)
- The maximal subgroups of classical algebraic groups (1987) (191)
- Flag-Transitive Subgroups of Chevalley Groups (1973) (162)
- The 2-transitive permutation representa-tions of the finite Chevalley groups (1976) (149)
- On finite rational groups and related topics (1989) (129)
- The Local Maximal Subgroups of Exceptional Groups of Lie Type, Finite and Algebraic (1992) (127)
- Reductive subgroups of exceptional algebraic groups (1996) (120)
- Finite groups with a split BN-pair of rank 1. II (1972) (109)
- Groups with a (B, N)-pair of rank 2. I (1973) (107)
- The maximal subgroups of positive dimension in exceptional algebraic groups (2004) (100)
- Maximal subgroups of exceptional algebraic groups (1991) (87)
- Unipotent elements, tilting modules, and saturation (2000) (80)
- On the subgroup structure of exceptional groups of Lie type (1998) (77)
- On the structure of parabolic subgroups (1990) (76)
- On finite subgroups of exceptional algebraic groups (1999) (73)
- Involutions in Chevalley groups over fields of even order (1976) (72)
- Subgroups generated by root elements in groups of Lie type (1994) (70)
- Some representations of exceptional Lie algebras (1988) (70)
- On the Overgroups of Irreducible Subgroups of the Finite Classical Groups (1987) (63)
- On groups with a standard component of known type. II (1981) (63)
- Anisotropic groups of type An and the commuting graph of finite simple groups (2002) (62)
- Finite groups having only one irreducible representation of degree greater than one (1968) (59)
- A survey of maximal subgroups of exceptional groups of Lie type (2002) (58)
- Fixed point ratios in actions of finite exceptional groups of lie type. (2002) (58)
- The root subgroups for maximal tori in finite groups of Lie type (1983) (57)
- Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable (2002) (57)
- On the Sims Conjecture and Distance Transitive Graphs (1983) (56)
- On the subgroup structure of classical groups (1998) (56)
- Subgroups of Algebraic Groups Containing Regular Unipotent Elements (1997) (51)
- Some Representations of Classical Groups (1975) (49)
- Selected papers of E.B. Dynkin with commentary (2000) (49)
- Finite and Locally Finite Groups (1995) (43)
- Modules for Algebraic Groups with Finitely Many Orbits on Subspaces (1997) (38)
- 2-Transitive groups in which the stabilizer of two points is cyclic☆ (1972) (38)
- Small rank permutation representations of finite Chevalley groups (1974) (37)
- Generators for Finite Simple Groups, with Applications to Linear Groups (1992) (36)
- Groups with a (B, N)-pair of rank 2. II (1974) (36)
- Generation of finite groups of Lie type (1982) (36)
- Subgroups of finite groups of Lie type (1979) (35)
- On the representation theory of the symmetric groups (1992) (35)
- Cross‐Characteristic Embeddings of Finite Groups of Lie Type (1990) (34)
- Extending morphisms from finite to algebraic groups (1990) (30)
- Representations and maximal subgroups of finite groups of Lie type (1988) (27)
- M-groups and the supersolvable residual (1969) (25)
- Factorizations of simple algebraic groups (1996) (25)
- Fixed point spaces in actions of exceptional algebraic groups (2002) (24)
- Bender groups as standard subgroups (1978) (20)
- Subgroups of exceptional algebraic groups which are irreducible on an adjoint or minimal module (2004) (20)
- The r-rank of the groups of exceptional Lie type (1986) (18)
- DOUBLE COSETS IN ALGEBRAIC GROUPS (1998) (18)
- Maximal Subgroups of Large Rank in Exceptional Groups of Lie Type (2005) (16)
- Outer unipotent classes in automorphism groups of simple algebraic groups (2014) (15)
- On finite groups whose Sylow subgroups are modular or quaternion-free (1969) (15)
- Abstract Homomorphisms of Algebraic Groups (1997) (14)
- On complements of $$\mathfrak{F}$$ -residuals in finite solvable groups (1970) (14)
- Unipotent centralizers in algebraic groups (2004) (13)
- Standard subgroups of type Ln(2a) (1977) (13)
- Variations on a theme of Steinberg (2003) (13)
- Some results on 2-transitive groups (1971) (11)
- Chevalley groups as standard subgroups, I (1979) (11)
- Unipotent subgroups of groups of Lie type (1983) (9)
- Topics in the Theory of Algebraic Groups (2005) (8)
- Subgroups of TypeA1Containing Semiregular Unipotent Elements (1997) (6)
- Maximal Subgroups of Finite Exceptional Groups (1998) (5)
- Distinguished unipotent elements and multiplicity-free subgroups of simple algebraic groups (2015) (5)
- On the Lie algebra of a finite group of Lie type (1982) (5)
- Parabolic subgroups containing the centralizer of a unipotent element (1983) (5)
- Subgroups of simple algebraic groups containing elements of fundamental subgroups (1999) (4)
- Groups, Combinatorics & Geometry: Subgroups of finite and algebraic groups (1992) (4)
- π-Groups that areM-groups (1972) (3)
- Multiplicity-free representations of algebraic groups (2021) (2)
- Some standard groups (1981) (2)
- Paleoseismic record of surface ruptures of the western third of the North Anatolian fault: Implications for fault segmentation models (2003) (1)
- Solvable groups having system normalizers of prime order (1973) (1)
- Tables of examples in low dimensions (2012) (0)
- Semiregular Unipotent Elements (1997) (0)
- Nilpotent elements in the other exceptional types (2012) (0)
- Classical groups in bad characteristic: Statement of results (2012) (0)
- Exceptional distinguished nilpotent elements (2012) (0)
- Classical groups in good characteristic (2012) (0)
- CHEVALLEY GROUPS AS STANDARD SUBGROUPS, III (2021) (0)
- Nilpotent classes and centralizers in (2012) (0)
- Corresponding unipotent and nilpotent elements (2012) (0)
- Annihilator spaces of nilpotent elements (2012) (0)
- Groups of Lie Type and their Geometries: Subgroups of exceptional algebraic groups (1995) (0)
- Finite classical groups (2012) (0)
- Step-by-step conjugation of p-subgroups of a group (1970) (0)
- Proofs of theorems 1, 2 and corollaries 3–8 (2012) (0)
- Exceptional groups: Statement of results for nilpotent elements (2012) (0)
- Unipotent elements in symplectic and orthogonal groups, =2 (2012) (0)
- Steele Prize for Mathematical Exposition (0)
- Multiplicity-free representations of algebraic groups II (2021) (0)
- Standard distinguished nilpotent elements (2012) (0)
- Tables of nilpotent and unipotent classes in the exceptional groups (2012) (0)
- Distinguished unipotent elements (2012) (0)
- Nilpotent elements: The symplectic and orthogonal cases, =2 (2012) (0)
- Non-distinguished unipotent classes (2012) (0)
- Reviews (2018) (0)
- Parabolic subgroups and labellings (2012) (0)
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