I. Martin Isaacs

I. Martin Isaacs's AcademicInfluence.com Rankings

I. Martin Isaacs

Mathematics

#5809

World Rank

#8146

Historical Rank

Group Theory

#47

World Rank

#60

Historical Rank

Measure Theory

#949

World Rank

#1236

Historical Rank

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Mathematics

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I. Martin Isaacs'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

Character Theory of Finite Groups (1976) (1670)
Finite Group Theory (2008) (355)
Characters of Solvable and Symplectic Groups (1973) (236)
Algebra, a graduate course (1994) (221)
Supercharacters and superclasses for algebra groups (2007) (214)
Characters of Π-separable groups (1984) (176)
Bounds for the Optimal Scheduling of n Jobs on m Processors (1964) (164)
A reduction theorem for the McKay conjecture (2007) (135)
Rings with Fixed-Point-Free Group Actions (1973) (107)
Sums of Element Orders in Finite Groups (2009) (95)
A CHARACTERIZATION OF GROUPS IN TERMS OF THE DEGREES OF THEIR CHARACTERS (1965) (93)
Characters of Groups Associated with Finite Algebras (1995) (92)
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras (2010) (87)
Finite Group Elements where No Irreducible Character Vanishes (1999) (78)
New refinements of the McKay conjecture for arbitrary finite groups (2002) (70)
Semipermutable π-subgroups (2014) (58)
Irreducible Character Degrees and Normal Subgroups (1997) (58)
Generalized Vandermonde determinants and roots of unity of prime order (1976) (58)
Counting characters of upper triangular groups (2007) (56)
Coprime Group Actions Fixing All Nonlinear Irreducible Characters (1989) (55)
Fong characters in π-separable groups (1986) (54)
Large orbits in actions of nilpotent groups (1999) (51)
Primitive characters, normal subgroups, andM-groups (1981) (50)
Weights and Vertices for Characters of π-Separable Groups (1995) (50)
Derived subgroups and centers of capable groups (2001) (47)
Induction and Restriction of π-Special Characters (1986) (47)
On the Probability That a Group Element is p-Singular (1995) (44)
Groups with Representations of Bounded Degree (1964) (40)
Automorphisms of matrix algebras over commutative rings (1980) (39)
Commutators and the Commutator Subgroup (1977) (38)
Character correspondences in solvable groups (1982) (37)
p-Supersolvability and actions on p-groups stabilizing certain subgroups (2014) (37)
The geometry of frieze patterns (1974) (35)
On groups of central type (1982) (35)
Half-Transitive Automorphism Groups (1966) (34)
On the Möbius function of a finite group (1989) (33)
Conjugacy in Groups of Upper Triangular Matrices (1998) (32)
The average degree of an irreducible character of a finite group (2013) (32)
Partial characters of π-separable groups (1991) (32)
Character Degrees and Derived Length of a Solvable Group (1975) (31)
Element orders and character codegrees (2011) (30)
Character correspondences and irreducible induction and restriction (1991) (29)
Conditions on p-subgroups implying p-nilpotence or p-supersolvability (2015) (29)
A note on groups of p-length 1∗ (1976) (29)
Equally partitioned groups. (1973) (28)
Lifting Brauer characters of $p$-solvable groups. (1974) (27)
On a theorem of Frobenius: solutions of X n = 1 in finite groups (1992) (27)
Lie algebras with self-centralizing ad-nilpotent elements (1979) (26)
Generating Symmetric Groups (1995) (25)
Degrees of sums in a separable field extension (1970) (25)
Groups with many equal classes (1970) (24)
On characters and fixed points of coprime operator groups (1990) (23)
Lifting Brauer characters of p-solvable groups, II (1978) (22)
Sets of $p$-powers as irreducible character degrees (1986) (22)
Characters of p′-Degree of p-Solvable Groups (2001) (22)
Irreducible Products of Characters (2000) (22)
Character restrictions and multiplicities in symmetric groups (2017) (22)
Characters of Solvable Groups (2018) (20)
Tensor induction of generalized characters and permutation characters (1983) (20)
Involutions and characters of upper triangular matrix groups (2005) (20)
Extensions of group representations over arbitrary fields (1981) (19)
Bounding the order of a group with a large character degree (2011) (18)
Abelian normal subgroups ofM-groups (1983) (18)
Recovering information about a group from its complex group algebra (1986) (18)
Character degree graphs and normal subgroups (2003) (18)
The π-character theory of solvable groups (1994) (17)
On the existence of ad-nilpotent elements (1977) (17)
Albert-Zassenhaus Lie algebras and isomorphisms☆ (1979) (17)
Characters and Hall Subgroups of Groups of Odd Order (1993) (17)
Complemented subgroups and p-nilpotence in finite groups (2012) (17)
Groups having at most three irreducible character degrees (1969) (16)
The p-parts of character degrees in p-solvable groups (1971) (16)
Geometry for College Students (2000) (16)
Inequalities for finite group permutation modules (2003) (15)
Solvable groups character degrees and sets of primes (1986) (15)
Groups with just one character degree divisible by a given prime (2009) (15)
Normal p-complements and fixed elements (2010) (15)
Fixed Points and Characters in Groups with Non-Coprime Operator Groups (1968) (15)
Permutation Group Subdegrees and the Common Divisor Graph (1993) (14)
Schur indices in finite groups (1975) (14)
Lie Algebras with Nilpotent Centralizers (1979) (14)
Blocks and subgroups (1972) (14)
Characters and Sets of Primes for Solvable Groups (1995) (14)
The Number of Generators of a Linear p-Group (1972) (14)
Groups whose irreducible representations have degrees dividing $p^{\mathrm{e}}$ (1964) (13)
Fixed point spaces, primitive character degrees and conjugacy class sizes (2006) (13)
The Character Degrees and Nilpotence Class of a p-Group☆☆☆ (2001) (13)
Sylow 2-subgroups of rational solvable groups (2012) (13)
Real characters of p′-degree (2004) (13)
Character sums and double cosets (2008) (13)
On the character theory of fully ramified sections (1983) (13)
Lie algebras with few centralizer dimensions (2003) (13)
Groups whose real irreducible characters have degrees coprime to p (2012) (13)
Complex p-Solvable linear groups (1973) (13)
Solution of Polynomials by Real Radicals (1985) (12)
Finite groups with small character degrees and large prime divisors. II. (1967) (12)
Blocks with Just Two Irreducible Brauer Characters in Solvable Groups (1994) (12)
Transfer and Tate’s theorem (2008) (12)
On the Poset of p‐SUBGROUPS of a p‐SOLVABLE GROUP (1988) (12)
Transitive permutation groups in which all derangements are involutions (2006) (11)
Squares of characters with few irreducible constituents in finite groups (1994) (11)
Fields of values of odd-degree irreducible characters (2019) (11)
Hall subgroup normalizers and character correspondences in $M$-groups (1990) (11)
Systems of equations and generalized characters in groups (1970) (11)
Subgroups generated by small classes in finite groups (2008) (10)
Groups with Distinct Monolithic Character Degrees (1999) (10)
Induction and Restriction of π-Partial Characters and their Lifts (1996) (10)
Derived Subgroups of Products of an Abelian and a Cyclic Subgroup (2004) (10)
Automorphisms fixing elements of prime order in finite groups (1997) (10)
Coprime Actions, Fixed-Point Subgroups and Irreducible Induced Characters (1996) (10)
Character degree sets that do not bound the class of a p-group (2002) (9)
p-groups having few almost-rational irreducible characters (2012) (9)
Extensions of group representations over nonalgebraically closed fields (1969) (9)
Class numbers of p-groups of a given order (2004) (9)
Orbit sizes, local subgroups and chains of p-groups (2001) (8)
Generalizations of Taketa’s theorem on the solvability of $M$-groups (1984) (8)
CAMINA p-groups that are generalized Frobenius complements (2014) (8)
Numbers of Classes and Chains of Subgroups In Finite Groups (1998) (8)
Counting objects which behave like irreducible Brauer characters of finite groups (1988) (8)
Generalizations of Fermat's Little Theorem via Group Theory (2005) (8)
Extensions of characters from Hall π-subgroups of π-separable groups (1985) (8)
Subgroups with the character restriction property (1986) (8)
Character stabilizer limits relative to a normal nilpotent subgroup (1986) (8)
Induced characters which are multiples of irreducibles (1989) (8)
Linear groups as stabilizers of sets (1977) (7)
Abelian point stabilizers in transitive permutation groups (2001) (7)
Characters of subnormal subgroups ofM-groups (1984) (7)
Solvable groups contain large centralizers (1986) (6)
Primitive characters of maximal subgroups of solvable groups (2010) (6)
Normalizers of nilpotent residuals (2017) (6)
Extensions of certain linear groups (1966) (6)
A note on $IC-p$ groups (1966) (6)
Real Fields and Repeated Radical Extensions (1997) (6)
Group elements and fields of character values (2009) (6)
Number of modular character degrees and lengths for solvable groups (1992) (6)
Groups with Relatively Few Non-Linear Irreducible Characters (1968) (5)
Repeated and final commutators in group actions (2012) (5)
Linear constituents of certain character restrictions (1998) (5)
DERIVED LENGTHS OF SOLVABLE GROUPS SATISFYING THE ONE-PRIME HYPOTHESIS. II (2001) (5)
Fixed points and π-complements in π-separable groups (1982) (5)
Invariant characters and coprime actions on finite nilpotent groups (2000) (5)
Character kernels and degree ratios in finite groups (2009) (5)
Constituents of Restricted and Induced Characters in Odd Order Groups (1995) (4)
Inductive sources and subnormal subgroups (2004) (4)
Invariant and extendible group characters (1970) (4)
Character tables and Sylow normalizers (2002) (4)
On a relation between the rank and the proportion of derangements in finite transitive permutation groups (2015) (4)
Nonexistence of partial traces for group actions (1981) (4)
On the number of elements that are not kth powers in a group (2015) (4)
Solvable groups having only three rational classes of 2-elements (2011) (4)
Large abelian normal subgroups (2018) (3)
Injective restriction of characters (2017) (3)
REPRESENTATIONS OF SOLVABLE GROUPS (LMS Lecture Note Series 185) (1995) (3)
An alternate proof of the Thompson replacement theorem (1970) (3)
Subgroups close to all of their conjugates (1990) (3)
Dual modules and group actions on extra-special groups (1988) (3)
Isomorphic subgroups of solvable groups (2015) (2)
Roots of Polynomials in Algebraic Extensions of Fields (1980) (2)
Two solvability theorems. (1967) (2)
Local functions on finite groups (2020) (2)
Brauer’s theorem (2006) (2)
Normal Subgroups with Nonabelian Quotients in p-Groups☆ (2002) (2)
Fields of values of Fong characters (2006) (2)
Fields generated by linear combinations of roots of unity, II. (1978) (2)
Counting maximal abelian subgroups of p-groups (2022) (2)
The minimal number of characters over a normal p-subgroup (2007) (1)
Rings, ideals, and modules (2009) (1)
A characteristic subgroup and kernels of Brauer characters (2005) (1)
Characters of groups having fixed-point-free automorphisms of 2-power order (2011) (1)
Changing the characteristic (2006) (1)
Products of characters (2006) (1)
Elementary Problems: E2908-E2913 (1981) (1)
Real representations of groups with a single involution (1977) (1)
Elementary Problems: E1243, E2440, E2652, E2665-E2670 (1977) (1)
Radical and cyclotomic extensions of the rational numbers (2007) (1)
Alperin's Conjecture and the Subgroup Structure of a Finite Group (2000) (1)
Induction and restriction of characters and Hall subgroups (2013) (1)
Problems: 10306-10313 (1993) (1)
The-Square-and-Add Markov Chain (2020) (1)
Fields generated by linear combinations of roots of unity (1977) (1)
Symmetric and Alternating Groups Generated by a Full Cycle and Another Element (2009) (1)
Group actions and orbits (2012) (1)
Subgroups and cosets (2009) (1)
The fixed-point-space dimension function for a finite group representation (1989) (1)
Upper bounds for the number of irreducible character degrees of a group (2014) (1)
Helmut Wielandt on subnormality (1994) (0)
More on subnormality (2008) (0)
Carter subgroups, characters and composition series (2022) (0)
T.I. sets and exceptional characters (2006) (0)
SOLUTIONS FOR FINITE GROUP THEORY BY I. MARTIN ISAACS (2012) (0)
Wittgenstein's philosophy of language (2005) (0)
Characters that agree on prime-power-order elements (2003) (0)
Separability and inseparability (2009) (0)
THE / >-PARTS OF CHARACTER DEGREES IN ^ SOLVABLE GROUPS (2012) (0)
Sylow 2-subgroups of rational solvable groups (2011) (0)
Group actions and orbits (2012) (0)
Letters to the editor (1965) (0)
On the number of elements that are not kth powers in a group (2015) (0)
Wittgenstein's tractatus and the limits of language (1999) (0)
Large abelian normal subgroups (2018) (0)
Irreducible constituents of faithful induced characters (2000) (0)
Artinian rings and projective modules (2009) (0)
The Schur index (2006) (0)
Injective restriction of characters (2017) (0)
Operator groups and unique decompositions (2009) (0)
Norms, traces, and discriminants (2009) (0)
Normalizers of nilpotent residuals (2016) (0)
EXTENSIONS OF GROUP REPRESENTATIONS OVER NONALGEBRAICALLY (2010) (0)
Changing the field (2006) (0)
Characters and integrality (2006) (0)
Algebras, modules, and representations (2006) (0)
Appendix. Some character tables (2006) (0)
A CHARACTERISTIC SUBGROUP AND KERNELS OF (2005) (0)
New groups from old (2009) (0)
Definitions and examples of groups (2009) (0)
Hall subgroups and fully extendible characters (2020) (0)
Algebraic sets and the Nullstellensatz (2009) (0)
Irreducible extensions of characters (2019) (0)
Solvable and nilpotent groups (2009) (0)
Book Review: Character theory of finite groups (1999) (0)
The Thompson subgroup (2008) (0)
Supercharacters, symmetric functions in noncommuting variables, extended abstract (2011) (0)
the Artin-Schreier theorem (2009) (0)
Module theory without rings (2009) (0)
Complemented subgroups and p-nilpotence in finite groups (2012) (0)
Cyclic intersections and control of fusion (2019) (0)
Semipermutable π-subgroups (2014) (0)
Elementary Problems: E3195-E3200 (1987) (0)
More transfer theory (2008) (0)
Simple modules and primitive rings (2009) (0)
Polynomial rings, PIDs, and UFDs (2009) (0)
THE TT-CHARACTER THEORY OF SOLVABLE GROUPS (2008) (0)
Language and Literacy in Multilingual Settings (2000) (0)
Blocks, character values, and centralizers of elements in solvable groups (1992) (0)
Roots, radicals, and real numbers (2009) (0)
The Sylow theorems and -groups (2009) (0)
An introduction to character theory (2009) (0)
CAMINA p-groups that are generalized Frobenius complements (2015) (0)
Group representations and characters (2006) (0)
Conditions on p-subgroups implying p-nilpotence or p-supersolvability (2015) (0)
Cyclotomy and geometric constructions (2009) (0)
p-groups having few almost-rational irreducible characters (2011) (0)
Complex p-solvable linear groups of finite order (2006) (0)
The average degree of an irreducible character of a finite group (2013) (0)
A Boolean algebra of characteristic subgroups of a finite group (2011) (0)
Chains of Normalizers of Subnormal Subgroups (2022) (0)

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What Schools Are Affiliated With I. Martin Isaacs?

I. Martin Isaacs is affiliated with the following schools:

University of Chicago
Harvard University

I. Martin Isaacs's Academic­Influence.com Rankings

Why Is I. Martin Isaacs Influential?

I. Martin Isaacs's Published Works

Published Works

What Schools Are Affiliated With I. Martin Isaacs?

I. Martin Isaacs's AcademicInfluence.com Rankings