New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
The Collected Mathematical Papers of Leonard Eugene Dickson
 SEARCH THIS BOOK:
AMS Chelsea Publishing
1975; 4022 pp; hardcover
Volume: 273
ISBN-10: 0-8284-0273-6
ISBN-13: 978-0-8284-0273-6
List Price: US$158 Member Price: US$142.20
Order Code: CHEL/273

The set of Collected Mathematical Papers of Leonard Eugene Dickson contains nearly all of his research papers and two of his books, the second being the famous Algebren und ihre Zahlentheorie. The work includes an annotated Bibliography and Index.

Part 1
• Determination of the structure of all linear homogeneous groups in a Galois field which are defined by a quadratic invariant
• Certain subgroups of the Betti-Mathieu group
• Canonical form of a linear homogeneous substitution in a Galois field
• Subgroups of order a power of $$p$$ in the general and special $$m$$-ary linear homogeneous groups in the $$GF[p^n]$$
• Distribution of the ternary linear homogeneous substitutions in a Galois field into complete sets of conjugate substitutions
• Representation of linear groups as transitive substitution groups
• Analytic functions suitable to represent substitutions
• Cyclic subgroups of the simple ternary linear fractional group in a Galois field
• Canonical form of a linear homogeneous transformation in an arbitrary realm of rationality
• Determination of the ternary modular groups
• On the quaternary linear homogeneous groups modulo $$p$$ of order a multiple of $$p$$
• On the canonical forms and automorphs of ternary cubic forms
• Rational reduction of a pair of binary quadratic forms; their modular invariants
• A theory of invariants
• Binary modular groups and their invariants
• Concerning the cyclic subgroups of the simple group $$G$$ of all linear fractional substitutions of determinant unity in two nonhomogeneous variables with coefficients in an arbitrary Galois field
• Invariantive reduction of quadratic forms in the $$GF[2^n]$$
• Finiteness of the odd perfect and primitive abundant numbers with $$n$$ distinct prime factors
• Even abundant numbers
• Invariantive theory of plane cubic curves modulo 2
• Determination of all groups of binary linear substitutions with integral coefficients taken modulo 3 and of determinant unity
• On the real elements of certain classes of geometrical configurations
• On the rank of a symmetrical matrix
• Ternary orthogonal group in a general field
• Groups defined for a general field by the rotation groups
• Lower limit for the number of sets of solutions of $$x^e +y^e +z^e \equiv 0\, (\text{mod } p)$$
• On the congruence $$x^n +y^n +z^n \equiv 0\, (\text{mod } p)$$
• Universal Waring theorems with cubic summands
• Universal forms $$a_{i}x^{n}_{i}$$ and Waring's problem
• Quaternary quadratic forms representing all integers
• Sur plusieurs groupes linéaires isomorphes au groupe simple d'ordre 25920
• Sur une généralisation du théorème de Fermat
• Some fallacies of an angle trisector
• A new solution of the cubic equation
• On systems of isothermal curves
• A matrix defined by the quaternion group
• A generalization of symmetric and skew-symmetric determinants
• A property of the group $$G_{2}^{2n}$$ all of whose operators except identity are of period 2
• On the factorization of large numbers
• On the representation of numbers as the sum of two squares [with M. Kaba]
• Amicable number triples
• Rational edged cuboids with equal volumes and equal surfaces
• Extensions of Waring's theorem on nine cubes
• A new method for universal Waring theorems with details for seventh powers
• Quadratic functions or forms, sums of whose values give all positive integers
• Projective classification of cubic surfaces, modulo 2
• The invariants, seminvariants and linear covariants of the binary quartic form modulo 2
• Fermat's last theorem and the origin and nature of the theory of algebraic numbers
• On quaternions and their generalization and the history of the eight square theorem
• Ternary quadratic forms and congruences
• A new definition of the general Abelian linear group
• Determination of an abstract simple group of order $$2^7 \cdot 3^6 \cdot 5\cdot 7$$ holoedrically isomorphic with a certain orthogonal group and with a certain hyperabelian group
• Index
Part 2
• Canonical forms of quaternary Abelian substitutions in an arbitrary Galois field
• Theory of linear groups in an arbitrary field
• On the group defined for any given field by the multiplication table of any given finite group
• The groups of Steiner in problems of contact
• On the reducibility of linear groups
• The groups of Steiner in problems of contact (second paper)
• Definitions of a field by independent postulates
• Definitions of a linear associative algebra by independent postulates
• On the subgroups of order a power of $$p$$ in the quaternary Abelian group in the Galois field of order $$p^n$$
• The subgroups of order a power of 2 of the simple quinary orthogonal group in the Galois field of order $$p^n =8l\pm 3$$
• On hypercomplex number systems
• The minimum degree $$\tau$$ of resolvents for the $$p$$-section of the periods of hyperelliptic functions of four periods
• On commutative linear algebras in which division is always uniquely possible
• Linear algebras in which division is always uniquely possible
• Invariants of binary forms under modular transformations
• Modular theory of group-matrices
• Representations of the general symmetric group as linear groups in finite and infinite fields
• Definite forms in a finite field
• General theory of modular invariants
• Linear algebras
• Proof of the finiteness of modular covariants
• Linear associative algebras and Abelian equations
• Quartic curves modulo 2
• Determination of all general homogeneous polynomials expressible as determinants with linear elements
• New division algebras
• Singular case of pairs of bilinear, quadratic, or Hermitian forms
• Simpler proofs of Waring's theorem on cubes, with various generalizations
• Construction of division algebras
• Waring's problem for cubic functions
• A new method for Waring theorems with polynomial summands
• Cyclotomy when $$e$$ is composite
• Cyclotomy and trinomial congruences
• A new method for Waring theorems with polynomial summands, II
• Some relations between the theory of numbers and other branches of mathematics
• Homogeneous polynomials with a multiplication theorem
• Linear algebras with associativity not assumed
• The ideal Waring theorem for twelfth powers
• On the inscription of regular polygons
• The analytic representation of substitutions on a power of a prime number of letters with a discussion of the linear group
• A generalization of Fermat's theorem
• An elementary exposition of Frobenius's theory of group-characters and group-determinants
• Index
Part 3
• Differential equations from the group standpoint
• On Waring's problem and its generalization
• The known systems of simple groups and their inter-isomorphisms
• The simplest model for illustrating the conic sections
• On the trisection of an angle and the construction of regular polygons of 7 and 9 sides
• Notes on the theory of numbers
• On the cyclotomic function
• Problems
• Generalizations of Waring's theorem on fourth, sixth, and eighth powers
• Minimum decompositions into $$n$$-th powers
• Two-fold generalizations of Cauchy's lemma
• Cyclotomy, higher congruences, and Waring's problem
• Cyclotomy, higher congruences, and Waring's problem, II
• Waring theorems of new type
• Proof of the ideal Waring theorem for exponents 7-180
• Solution of Waring's problem
• Universal Waring theorems
• The structure of the linear homogeneous groups defined by the invariant
• The alternating group on eight letters and the quaternary linear congruence group modulo two
• The hyperorthogonal groups
• Universal Waring theorem for eleventh powers
• Arithmetic of quaternions
• The rational linear algebras of maximum and minimum ranks
• The straight lines on modular cubic surfaces
• Recent progress in the theories of modular and formal invariants and in modular geometry
• Quaternions and their generalizations
• Quadratic forms which represent all integers
• Polygonal numbers and related Waring problems
• New Waring theorems for polygonal numbers
• Congruences involving only $$e$$-th powers
• Outline of the theory to date of the arithmetics of algebras
• Further development of the theory of arithmetics of algebras
• A new theory of linear transformations and pairs of bilinear forms
• On the minimum degree of resolvents for the $$p$$-section of the periods of hyperelliptic functions of four periods
• On the theory of numbers and generalized quaternions
• Algebraic theory of the expressibility of cubic forms as determinants, with application to Diophantine analysis
• On finite algebras
• Index
Part 4
• Algebren und ihre Zahlentheorie
• The structure of certain linear groups with quadratic invariants
• The group of linear homogeneous substitutions on $$mq$$ variables which is defined by the invariant
• Concerning the four known simple linear groups of order 25920, with an introduction to the hyper-abelian linear groups
• The abstract group isomorphic with the symmetric group on $$k$$ letters
• An abstract simple group of order 25920
• Linear substitutions commutative with a given substitution
• Concerning the Abelian and related linear groups
• Generational relations for the abstract group simply isomorphic with the linear fractional group in the $$GF[2^n]$$
• Linear groups in an infinite field
• A quadratic Cremona transformation defined by a conic
• Two systems of subgroups of the quaternary Abelian group in a general Galois field
• On the subgroups of order a power of $$p$$ in the linear homogeneous and fractional groups in the $$GF[p^n]$$
• On the class of the substitutions of various linear groups
• The group of a tactical configuration
• A general theorem on algebraic numbers
• Proof of the existence of the Galois field of order $$p^r$$ for every integer $$r$$ and prime number $$p$$
• The symmetric group on eight letters and the senary first hypoabelian group
• On quadratic forms in a general field
• On triple algebras and ternary cubic forms
• Criteria for the irreducibility of a reciprocal equation
• Modular theory of group characters
• On higher congruences and modular invariants
• On the factorization of integral functions with $$p$$-adic coefficients
• On the representation of numbers by modular forms
• On the negative discriminants for which there is a single class of positive primitive binary quadratic forms
• Invariants, seminvariants, and covariants of the ternary and quaternary quadratic form modulo 2
• On the relation between linear algebras and continuous groups
• Mathematics in war perspective. [Presidential address delivered before the American Mathematical Society, December 27, 1918.]
• Fallacies and misconceptions in Diophantine analysis
• A new method in Diophantine analysis
• Index
Part 5
• Recent progress on Waring's theorem and its generalizations
• Proof of a Waring theorem on fifth powers
• Waring's problem for ninth powers
• The converse of Waring's problem
• The Waring problem and its generalizations
• A generalization of Waring's problem
• All integers except 23 and 239 are sums of eight cubes
• The theory of numbers: its principal branches
• Recent light on classic problems in the theory of numbers
• Systems of simple groups derived from the orthogonal group
• Systems of simple groups derived from the orthogonal group
• Why it is impossible to trisect an angle or to construct a regular polygon of seven or nine sides by ruler and compasses
• Systems of continuous and discontinuous simple groups
• Higher irreducible congruences
• The structure of the hypoabelian groups
• Report on the recent progress in the theory of linear groups
• Orthogonal group in a Galois field
• Concerning a linear homogeneous group in $$C_{m, q}$$ variables isomorphic to the general linear homogeneous group in $$m$$ variables
• Systems of simple groups derived from the orthogonal group
• Concerning real and complex continuous groups
• The configurations of the 27 lines on a cubic surface and the 28 bitangents to a quartic curve
• An extension of the theory of numbers by means of correspondences between fields
• Integral solutions of $$x^2-my^2=zw$$
• All integral solutions of $$ax^2 + bxy + cy^2 =w_{1}w_{2}\cdots w_{n}$$
• A generalization of Waring's theorem on nine cubes
• Integers represented by positive ternary quadratic forms
• Extensions of Waring's theorem on fourth powers
• All positive integers are sums of values of a quadratic function of $$x$$
• Generalizations of the theorem of Fermat and Cauchy on polygonal numbers
• Extended polygonal numbers
• New division algebras
• The forms $$ax^2 + by^2 + cz^2$$ which represent all integers
• Perfect and amicable numbers
• Cyclic numbers
• Proof of the non-isomorphism of the simple Abelian group on $$2m$$ indices and the simple orthogonal group on $$2m +1$$ indices for $$m>2$$
• A triply infinite system of simple groups
• The first hypoabelian group generalized
• A class of groups in an arbitrary realm connected with the configuration of the 27 lines on a cubic surface
• Theorems on the residues of multinomial coefficients with respect to a prime modulus
• Determination of all the subgroups of the three highest powers of $$p$$ in the group $$G$$ of all $$m$$-ary linear homogeneous transformations modulo $$p$$
• On the last theorem of Fermat
• On the last theorem of Fermat (second paper)
• On families of quadratic forms in a general field
• On non-vanishing forms
• Theorems and tables on the sum of the divisors of a number
• On commutative linear groups
• Modular invariants of the system of a binary cubic, quadratic, and linear form
• Gergonne's pile problem
• Isomorphism between certain systems of simple linear groups
• Impossibility of restoring unique factorization in a hypercomplex arithmetic
• Algebras and their arithmetics
• Quadratic fields in which factorization is always unique
• Resolvent sextics of quintic equations
• Obituary: Hans Frederik Blichfeldt 1873-1945
• Bibliography
• Index
Part 6
• Algebraic invariants
• Simplicity of the Abelian group on two pairs of indices in the Galois field of order $$2^{n}, n>1$$
• A class of linear groups including the Abelian group
• The abstract form of the special linear homogeneous group in an arbitrary field
• The abstract form of the Abelian linear groups
• A class of groups in an arbitrary realm connected with the configuration of the 27 lines on a cubic surface [Second paper]
• Note on modular invariants
• Les polynomes égaux à des déterminants
• La composition des polynomes
• The largest linear homogeneous groups with an invariant Pfaffian
• The known finite simple groups
• On the groups defined for an arbitrary field by the multiplication tables of certain finite groups
• The abstract group simply isomorphic with the group of linear fractional transformations in a Galois field
• Generational relations of an abstract simple group of order 4080
• Invariants of the general quadratic form modulo 2
• Modular invariants of a general system of linear forms
• Invariantive classification of pairs of conics modulo 2
• Definition of the Abelian, the two hypoabelian, and related linear groups of the groups of isomorphism of certain elementary groups
• Determination of all the subgroups of the known simple group of order 25920
• Definition of a group and a field by independent postulates
• On semi-groups and the general isomorphism between infinite groups
• On quadratic, Hermitian and bilinear forms
• Equivalence of pairs of bilinear or quadratic forms under rational transformation
• An invariantive investigation of irreducible binary modular forms
• A fundamental system of invariants of the general modular linear group with a solution of the form problem
• Invariants in the theory of numbers
• On the number of inscriptible regular polygons
• Three sets of generational relations defining the abstract simple group of order 504
• Generational relations defining the abstract simple group, of order 660
• The abstract group $$G$$ simply isomorphic with the alternating group on six letters
• Criteria for the irreducibility of functions in a finite field
• On the theory of equations in a modular field
• On binary modular groups and their invariants
• Geometrical and invariantive theory of quartic curves modulo 2
• A quadratic Cremona transformation defined by a conic
• Factors of a certain determinant of order six
• The order of a certain senary linear group
• Three algebraic notes
• Note on the volume of a tetrahedron in terms of the coordinates of the vertices