The collected mathematical papers of Leonard Eugene Dickson.
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| Author / Creator: | Dickson, Leonard E. (Leonard Eugene), 1874-1954 |
|---|---|
| Imprint: | Bronx, N.Y., Chelsea Pub. Co. [1975-1983] |
| Description: | 6 v. illus. 26 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/35451 |
Table of Contents:
- 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 lineaires isomorphes au groupe simple d'ordre 25920
- Sur une generalisation du theoreme 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
- Universal quadratic 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
- Additive number theory for all quadratic functions
- 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 [P2esidential 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
- The quadratic Cremona transformation 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 egaux a des determinants 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
- Rational triangles and quadrilaterals
- The points of inflexion of a plane cubic curve Reducible cubic forms expressible rationally as determinants
- A fundamental system of covariants of the ternary cubic form
- A new simple theory of hypercomplex integers Algebres nouvelles de division Memoir on Abelian transformations
- Application of groups to a complex problem in arrangements Note on cubic equations and congruences
- A class of simply transitive linear groups Fields whose elements are linear differential expressions
- Bibliography
- Index
