Determination of the structure of all linear homogeneous groups in a Galois field which are defined by a quadratic invariant / Part 1: |
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 |
Canonical forms of quaternary Abelian substitutions in an arbitrary Galois field / Part 2: |
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 |
Differential equations from the group standpoint / Part 3: |
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 |
Algebren und ihre Zahlentheorie / Part 4: |
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 |
Recent progress on Waring's theorem and its generalizations Proof of a Waring theorem on fifth powers / Part 5: |
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 |
Algebraic invariants Simplicity of the Abelian group on two pairs of indices in the Galois field of order $2^{n}, n>1$ / Part 6: |
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 |