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 |