Robert Guralnick | Academic Influence

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Robert Guralnick

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Measure Theory

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Mathematics

Robert Guralnick's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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According to Wikipedia, Robert Michael Guralnick is an American mathematician known for his work in group theory. He works as a Professor of Mathematics at the University of Southern California. Guralnick was named a Fellow of the American Mathematical Society in 2012, was an invited lecturer at the International Congress of Mathematicians in 2014, and was awarded the Cole Prize in 2018. He is currently managing editor of Forum of Mathematics.

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Robert Guralnick'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

Subgroups of prime power index in a simple group (1983) (327)
Some applications of the first cohomology group (1984) (202)
Probabilistic Generation of Finite Simple Groups (2000) (147)
Probabilistic generation of finite simple groups, II (2000) (140)
Expansion in finite simple groups of Lie type (2013) (135)
Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements (2009) (130)
ON THE COMMUTING PROBABILITY IN FINITE GROUPS (2006) (129)
Linear Groups with Orders Having Certain Large Prime Divisors (1999) (118)
Generation of finite almost simple groups by conjugates (2003) (104)
Schur covers and Carlitz’s conjecture (1993) (91)
Simple groups admit Beauville structures (2010) (88)
Products of conjugacy classes and fixed point spaces (2010) (87)
A note on commuting pairs of matrices (1992) (85)
On the Minimal Degree of a Primitive Permutation Group (1998) (82)
Indecomposable Set-Theoretical Solutions to the Quantum Yang–Baxter Equation on a Set with a Prime Number of Elements (2000) (82)
The rational function analogue of a question of Schur and exceptionality of permutation representations (2002) (77)
Low‐Dimensional Representations of Special Linear Groups in Cross Characteristics (1999) (73)
Finite groups of genus zero (1990) (64)
Cross characteristic representations of even characteristic symplectic groups (2004) (61)
Cross characteristic representations of symplectic and unitary groups (2002) (60)
Commuting pairs and triples of matrices and related varieties (2000) (58)
The probability of generating a classical group (1994) (58)
Finite simple unisingular groups of Lie type (2003) (56)
On p-singular elements in Chevalley groups in characteristic ρ (2001) (55)
On base sizes for symmetric groups (2011) (55)
ON ABELIAN QUOTIENTS OF PRIMITIVE GROUPS (1989) (53)
Special issue celebrating the 80th birthday of Robert Steinberg (2003) (53)
Module equivalences: Local to global when primitive polynomials represent units (1982) (52)
Presentations of finite simple groups: a quantitative approach (2006) (50)
Thompson-like characterizations of the solvable radical ✩ (2006) (48)
Derangements in simple and primitive groups (2002) (47)
Sets of elements that pairwise generate a linear group (2008) (45)
Small Representations Are Completely Reducible (1999) (44)
On fixed points of permutations (2007) (42)
Subgroups inducing the same permutation representation, II (1983) (41)
Self-normalizing Sylow subgroups (2003) (41)
Bounds for fixed point free elements in a transitive group and applications to curves over finite fields (1997) (41)
Presentations of Finite Simple Groups: Profinite and Cohomological Approaches (2007) (41)
Decompositions of small tensor powers and Larsen’s conjecture (2005) (41)
Strongly dense free subgroups of semisimple algebraic groups (2010) (40)
The First Cohomology Group and Generation of Simple Groups (1998) (38)
Invertible preservers and algebraic groups (1994) (38)
Modules for Algebraic Groups with Finitely Many Orbits on Subspaces (1997) (38)
SIMPLE GROUPS STABILIZING POLYNOMIALS (2013) (37)
Solvable generation of groups and Sylow subgroups of the lower central series (1982) (36)
Generation of simple groups (1986) (35)
Exceptional Covers and Bijections on Rational Points (2005) (34)
Commutators and commutator subgroups (1982) (34)
The non-coprime k(GV) problem (2005) (33)
Oort groups and lifting problems (2007) (33)
Hamiltonian cycles in the generating graphs of finite groups (2009) (33)
Products of conjugacy classes in finite and algebraic simple groups (2012) (32)
Shirshov’s theorem and representations of semigroups (1997) (32)
Monodromy Groups of Coverings of Curves (2003) (32)
Presentations of finite simple groups: a computational approach (2008) (31)
On base sizes for algebraic groups (2013) (31)
Alternating forms and self-adjoint operators (2007) (31)
On extensions of the Baer-Suzuki Theorem (1993) (30)
On a result of Schur (1979) (30)
The spread of a finite group (2020) (30)
On the Spread of Finite Simple Groups (2003) (30)
Roth's theorems and decomposition of modules (1981) (30)
Conjugacy class properties of the extension of GL(n,q) generated by the inverse transpose involution (2003) (30)
First cohomology groups of Chevalley groups in cross characteristic (2011) (29)
Groups of Lie Type and their Geometries: Monodromy groups of polynomials (1995) (29)
Orders of Finite Groups of Matrices (2005) (29)
The dimension of the first cohomology group (1986) (28)
Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I: Generic Covers and Covers with Many Branch Points (2007) (28)
Pseudosimilarity and cancellation of modules (1982) (27)
Symmetric powers and a problem of Kollár and Larsen (2008) (27)
Average dimension of fixed point spaces with applications (2010) (27)
Derived subgroups of fixed points (2001) (26)
Invertible preservers and algebraic groups III: preservers of unitary similarity (congruence) invariants and overgroups of some unitary subgroups ∗ (1997) (26)
Permutation polytopes and indecomposable elements in permutation groups (2005) (26)
On the number of generators of a finite group (1989) (26)
A note on pairs of matrices with rank one commutator (1979) (26)
Frobenius-Schur indicators for subgroups and the Drinfel’d double of Weyl groups (2007) (25)
Exceptional Polynomials of Affine Type (1997) (25)
The local lifting problem for actions of finite groups on curves (2009) (25)
The Automorphism Groups of a Family of Maximal Curves (2011) (24)
A new family of exceptional polynomials in characteristic two (2007) (24)
Normalizers of Primitive Permutation Groups (2016) (24)
Classification of 2F-modules, I (2002) (23)
Adequate subgroups (2011) (23)
Squaring a conjugacy class and cosets of normal subgroups (2015) (23)
The Probability of Generating a Finite Soluble Group (2000) (23)
Derangements in finite classical groups for actions related to extension field and imprimitive subgroups and the solution of the Boston–Shalev conjecture (2015) (23)
A new solvability criterion for finite groups (2010) (23)
Structure of algebras (1980) (23)
Derangements in subspace actions of finite classical groups (2013) (22)
Lifting in Frattini Covers and A Characterization of Finite Solvable Groups (2011) (22)
Some Applications of Subgroup Structure to Probabilistic Generation and Covers of Curves (1998) (22)
Representation Growth in positive characteristic and conjugacy classes of maximal subgroups (2010) (22)
Effective results on the Waring problem for finite simple groups (2013) (21)
A note on the local-global principle for similarity of matrices (1980) (21)
Characterizations of the solvable radical (2009) (21)
Lifting homomorphisms of modules (1985) (19)
Roth's theorems for sets of matrices (1985) (19)
Surjective word maps and Burnsides $p^aq^b$ theorem (2015) (19)
Similarity of matrices over local rings (1981) (19)
Galois groups and the multiplicative structure of field extensions (1992) (18)
Base sizes for S-actions of finite classical groups (2014) (18)
Polynomials with PSL(2) monodromy (2007) (18)
On rational and concise words (2014) (18)
Zeroes of permutation characters with applications to prime splitting and Brauer groups (1990) (18)
CHARACTER LEVELS AND CHARACTER BOUNDS (2017) (17)
Random Generation of Finite Simple Groups (1999) (17)
Eigenvalues of Symmetrical Matrices and Graphs (1994) (16)
Multiplicative maps on invertible matrices that preserve matricial properties (2003) (16)
Matrix equivalence and isomorphism of modules (1982) (16)
Real class sizes and real character degrees (2010) (16)
Minimal polynomials of integral symmetric matrices (1993) (16)
Biperfect Hopf Algebras (1999) (15)
Polynomial rings over Goldie rings are often Goldie (1986) (15)
Low Degree Representations of Simple Lie Groups (2010) (15)
The number of regular semisimple conjugacy classes in the finite classical groups (2012) (15)
Rational rigidity for ${E}_{8}(p)$ (2012) (15)
Sylow p‐Subgroups and Subnormal Subgroups of Finite Groups (1993) (15)
Corrigendum to "Sets of elements that pairwise generate a linear group" [J. Combin. Theory Ser. A 115 (3) (2008) 442-465] (2011) (15)
Power cancellation of modules. (1986) (15)
Inequalities for finite group permutation modules (2003) (15)
The genus of a module II. Roiter's theorem, power cancellation and extension of scalars (1987) (15)
On orbital partitions and exceptionality of primitive permutation groups (2004) (15)
Frobenius subgroups of free profinite products (2010) (14)
Cancellation and direct summands in dimension 1 (1991) (14)
On a subfactor generalization of Wallʼs conjecture (2010) (14)
Automorphisms of the Modular Curve (2005) (14)
Spinors and essential dimension (2016) (14)
Enumeration of Commuting Pairs in Lie Algebras over Finite Fields (2016) (13)
On groups with decomposable commutator subgroups (1978) (13)
On the Picard group: torsion and the kernel (1994) (13)
Invertible Preservers and Algebraic Groups II: Preservers of Similarity Invariants and Overgroups of PSLn (F) (1997) (13)
Surjective word maps and Burnside’s $$p^aq^b$$paqb theorem (2015) (12)
Presentations of modules when ideals need not be principal (1988) (12)
Equations in prime powers (1985) (12)
A problem of Kollar and Larsen on finite linear groups and crepant resolutions (2010) (12)
Rational rigidity for E8(p) (2014) (12)
Cross characteristic representations of odd characteristic symplectic groups and unitary groups (2006) (12)
Burnside-Type Problems Related to Solvability (2007) (12)
Variations on the Baer–Suzuki theorem (2013) (11)
Symmetric and alternating powers of Weil representations of finite symplectic groups (2018) (11)
Cancellation counterexamples in Krull dimension 1 (1990) (11)
Intersections of conjugacy classes and subgroups of algebraic groups (2006) (11)
Asymptotics of the number of involutions in finite classical groups (2016) (11)
ELEMENTARY DIVISOR THEOREM FOR NONCOMMUTATIVE PIDS (1988) (11)
Generic stabilizers in actions of simple algebraic groups I: modules and the first Grassmanian varieties (2019) (10)
Coprime subdegrees for primitive permutation groups and completely reducible linear groups (2011) (10)
On a question of B. H. Neumann (2002) (10)
On invertible bimodules and automorphisms of noncommutative rings (1994) (10)
The rank of a commutator (1983) (10)
Expressing group elements as commutators (1980) (9)
Irreducible polynomials which are locally reducible everywhere (2005) (9)
On the cohomology of alternating and symmetric groups and decomposition of relation modules (1990) (9)
The 2F-modules for nearly simple groups (2007) (9)
Essential dimension of algebraic groups, including bad characteristic (2015) (9)
Groups, Combinatorics & Geometry: Primitive permutation characters (1992) (9)
The genus of a module (1984) (9)
Adequate subgroups and indecomposable modules (2014) (8)
Representations under ring extensions: Latimer-MacDuffee and Taussky correspondences (1984) (8)
Groups, Combinatorics & Geometry: The genus of a permutation group (1992) (8)
Adequate subgroups II (2011) (8)
Groups with exactly one irreducible character of degree divisible by p (2014) (8)
Similarity of holomorphic matrices (1988) (8)
Endomorphism fields of abelian varieties (2016) (8)
Global Oort Groups (2015) (7)
Automorphic realization of residual Galois representations (2010) (7)
Cyclic Quotients of Transitive Groups (2000) (7)
Thompson-like characterization of the solvable radical (2005) (7)
Generic stabilizers in actions of simple algebraic groups II: higher Grassmannian varieties (2019) (7)
Rigid local systems and alternating groups (2017) (7)
Generically free representations, I: large representations (2017) (7)
Multiplicative groups of fields modulo products of subfields (1996) (7)
Inversion invariant additive subgroups of division rings (2006) (7)
Products and commutators of classes in algebraic groups (2013) (6)
On cyclic commutator subgroups (1978) (6)
Cosets of Sylow p-subgroups and a question of Richard Taylor (2012) (6)
Exceptional Polynomials over Arbitrary Fields (2004) (6)
The direct product theorem for profinite groups (2006) (6)
GENERICALLY FREE REPRESENTATIONS III: EXTREMELY BAD CHARACTERISTIC (2018) (6)
Invariants of finite linear groups on relatively free algebras (1985) (6)
Projective modules with free multiples and powers (1986) (6)
Finite groups with odd Sylow normalizers (2016) (6)
Subgroup growth in some pro- groups (2001) (6)
Stable Subnorms II (2003) (6)
PERMUTABILITY OF CHARACTERS ON ALGEBRAS (1997) (6)
Reduction theorems for groups of matrices (2004) (5)
FROBENIUS GROUPS AS MONODROMY GROUPS (2008) (5)
Globally irreducible Weyl modules (2016) (5)
A stable range for quadratic forms over commutative rings (1997) (5)
Incidence Matrices, Permutation Characters, and the Minimal Genus of a Permutation Group (2002) (5)
Similarity of matrices over commutative rings (1991) (5)
The Waring Problem for Finite Quasisimple Groups. II (2013) (5)
Adequate groups of low degree (2013) (5)
Isomorphism of modules under ground ring extensions (1982) (5)
Variants of some of the Brauer-Fowler theorems (2018) (5)
Conjugacy classes, characters and products of elements (2018) (5)
Solitary Galois Extensions of Algebraic Number Fields (1995) (5)
Sectional rank and cohomology (2018) (5)
GENERICALLY FREE REPRESENTATIONS II: IRREDUCIBLE REPRESENTATIONS (2017) (5)
On the singular value decomposition over finite fields and orbits of GU×GU (2021) (4)
Remarks on Proficient groups (2009) (4)
Essential dimension of exceptional groups, including bad characteristic (2015) (4)
Simple algebraic groups are (usually) determined by an invariant (2013) (4)
Generically free representations III: exceptionally bad characteristic (2018) (4)
A question of stafford about affine pi algebras (1990) (4)
Nonexistence of partial traces for group actions (1981) (4)
Generation of the lower central series II (1984) (4)
Topological generation of simple algebraic groups (2021) (4)
Conjugacy classes of derangements in finite transitive groups (2016) (4)
Appendix A: Adequacy of representations of finite groups of Lie type (2012) (4)
On a relation between the rank and the proportion of derangements in finite transitive permutation groups (2015) (4)
A lower bound for the dimension of a highest weight module (2016) (4)
On isometry groups of self-adjoint traceless and skew-symmetric matrices (2017) (4)
Real constituents of permutation characters (2020) (3)
On the generalized Fitting height and insoluble length of finite groups (2019) (3)
Zero-one generation laws for finite simple groups (2018) (3)
Subfields of Algebraically Closed Fields (1977) (3)
Primitive monodromy groups of genus at most two (2014) (3)
Character Levels and Character Bounds. II (2019) (3)
Nonisomorphic curves that become isomorphic over extensions of coprime degrees (2008) (3)
Generation of the lower central series (1982) (3)
Addendum to paper “On the commuting probability in finite groups” by R.M. Guralnick and G.R. Robinson [J. Algebra 300 (2) (2006) 509–528] (2008) (3)
A remark concerning unipotent matrix groups (1979) (3)
Fixed point ratios for finite primitive groups and applications (2021) (3)
Reducibility of nilpotent commuting varieties (2013) (3)
Topological generation of exceptional algebraic groups (2019) (3)
Matrices over differential fields which commute with their derivative (1993) (3)
Normalizing elements in PI rings (1995) (2)
WEAKLY CLOSED UNIPOTENT SUBGROUPS IN CHEVALLEY GROUPS (2005) (2)
Generic stabilizers associated with a peculiar half-spin representation. Appendix to: SPINORS AND ESSENTIAL DIMENSION by S. Garibaldi and R. Guralnick (2017) (2)
Maximal subfields of algebraically closed fields (1980) (2)
On the maximal number of coprime subdegrees in finite primitive permutation groups (2012) (2)
Characteristic polynomials of automorphisms of hyperelliptic curves (2008) (2)
Centers of Sylow subgroups and automorphisms (2019) (2)
Not all quadrative norms are strongly stable (2001) (2)
Irreducibility of Weyl Modules over Fields of Arbitrary Characteristic (2016) (2)
Permutation representations of nonsplit extensions involving alternating groups (2017) (2)
Polynomials with $\operatorname{PSL}(2)$ monodromy (2010) (2)
Characteristic Polynomials and Fixed Spaces of Semisimple Elements (2011) (2)
Torsion in the Picard group and extension of scalars (1988) (2)
Rational Maps and Images of Rational Points of Curves over Finite Fields (2003) (2)
Finite Simple Groups: Thirty Years of the Atlas and Beyond (2017) (2)
A Question about Pic(X) as a G-module (2004) (2)
Subgroups of GLn(q) which fix sublattices of the subspace lattice (2003) (2)
Strongly dense free subgroups of semisimple algebraic groups (2012) (1)
Generic Stabilizers for Simple Algebraic Groups (2021) (1)
Normalizing elements of the trace ring of generic matrices (1989) (1)
Galois Groups and Fundamental Groups Msri Publications (2004) (1)
Cohen Lenstra Partitions and Mutually Annihilating Matrices over a Finite Field (2021) (1)
Preface to the 12th ILAS Conference Proceedings, Regina 2005 (2007) (1)
A note on abelian subgroups of maximal order (2018) (1)
Bass units as free factors in integral group rings of simple groups (2013) (1)
Elementary abelian 2-subgroups of Sidki-type in finite groups (2007) (1)
Modules under ground ring extension (1985) (1)
On the singular value decomposition over finite fields and orbits of GU x GU (2018) (1)
Nil subrings of endomorphism rings of finitely generated modules over affine PI-rings (2010) (1)
Coprime automorphisms of finite groups (2021) (1)
On invariable generation of alternating groups by elements of prime and prime power order (2022) (1)
On the commuting probability of p-elements in a finite group (2021) (1)
On cyclic commutator subgroups (1978) (1)
Special issue in memory of Kay Magaard (2020) (1)
The Asymptotic Genus of a Group (2004) (0)
UNIPOTENT SUBGROUPS OF STABILIZERS (2022) (0)
Criteria for solubility and nilpotency of finite groups with automorphisms (2022) (0)
Rational Rigidity for Some Exceptional Groups (2012) (0)
REPORT ON BIRS WORKSHOP PERMUTATION GROUPS (13W5033) – 21–26 JULY 2013 (2013) (0)
Commuting involutions and elementary abelian subgroups of simple groups (2020) (0)
Endomorphism fields of abelian varieties (2017) (0)
Surjective word maps and Burnside’s paqb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p^aq^b$$\end{document} theorem (2018) (0)
Base sizes for S-actions of finite classical groups (2013) (0)
Variations on the Baer–Suzuki theorem (2014) (0)
Jordan Triple Systems in Complex and Functional Analysis (2020) (0)
Book Review: Unipotent and nilpotent classes in simple algebraic groups and Lie algebras (2014) (0)
generation of exceptional algebraic groups. Advances in Mathematics, (2020) (0)
Jan Saxl, 5 June 1948 – 2 May 2020 (2022) (0)
REALIZATION OF RESIDUAL GALOIS REPRESENTATIONS (2008) (0)
On an identity of Schur (1983) (0)
APPENDIX : ADEQUATE SUBGROUPS 59 APPENDIX : ADEQUATE SUBGROUPS (2010) (0)
Coprime subdegrees for primitive permutation groups and completely reducible linear groups (2012) (0)
On the maximal number of coprime subdegrees in finite primitive permutation groups (2016) (0)
Essential dimension of algebraic groups, including bad characteristic (2016) (0)
Relative Brauer groups of global fields (1983) (0)
AUTOMORPHISMS OF HYPERELLIPTIC MODULAR CURVES X 0 ( N ) IN POSITIVE (2009) (0)
Enumeration of conjugacy classes in affine groups (2021) (0)
A remark on infinite torsion groups with periodic cohomology (1992) (0)
J an 2 01 9 ON THE SINGULAR VALUE DECOMPOSITION OVER FINITE FIELDS AND ORBITS OF GU (2019) (0)
The Work of John Griggs Thompson: A Survey (2014) (0)
A pr 2 00 4 IRREDUCIBLE POLYNOMIALS WHICH ARE LOCALLY REDUCIBLE EVERYWHERE (2004) (0)
Simple Lie groups stabilizing G-invariant norms (2021) (0)
Procducts of commutators and classes in algebraic groups (2013) (0)
Polynomials which are locally reducible (2004) (0)
Rigidity for F_4(p) (2015) (0)
2 Recent Developments and Open Problems (2009) (0)
On the generation of simple groups by Sylow subgroups (2022) (0)
On cyclic commutator subgroups (1978) (0)
Special issue in honor of Susan Montgomery (2010) (0)
On cyclic commutator subgroups (1979) (0)
Reviews (2018) (0)
Cross characteristic representations of odd characteristic symplectic groups and unitary groups (vol 299, pg 443, 2006) (2006) (0)
Contemporary Mathematics Orders of Finite Groups of Matrices (2005) (0)
Certain subgroups of Weyl groups are split (2010) (0)
Commentary on “A brief history of the classification of the finite simple groups” by Ronald Solomon (2018) (0)
Strongly base-two groups (2022) (0)
Enumeration of Commuting Pairs in Lie Algebras over Finite Fields (2018) (0)
On the Fitting height and insoluble length of finite groups (2019) (0)
GROUPS WITH EXACTLY TWO SUBGROUPS OF GIVEN ORDER (2002) (0)
Genus Class Groups and Separable Base Change (2017) (0)
ON “ A BRIEF HISTORY OF THE CLASSIFICATION OF THE FINITE SIMPLE GROUPS ” BY (2018) (0)
Conjugacy classes of derangements in finite transitive groups (2016) (0)
Products and commutators of classes in algebraic groups (2014) (0)
Finite groups can be generated by a pi-subgroup and a pi'-subgroup (2021) (0)
Permutation representations of nonsplit extensions involving alternating groups (2018) (0)
Maximal Subgroups of Finite Groups (2012) (0)
Permutation Groups (2009) (0)
Globally Irreducible Weyl Modules for Quantum Groups (2016) (0)
APPENDIX : ADEQUATE SUBGROUPS (2011) (0)

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