| 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 |
