Any finite group of linear transformations on n variables leaves invariant a positive definite Hermitian form, and can therefore be expressed, after a suitable change of variables, as a group of unitary transformations (5, p. 257). Such a group may be thought of as a group of congruent transformations, keeping the origin fixed, in a unitary space Un of n dimensions, in which the points are specified by complex vectors with n components, and the distance between two points is the norm of the difference between their corresponding vectors.

Finite Unitary Reflection Groups

http://www-math.mit.edu/~rstan/pubs/pubfiles/30.pdf

Hilbert functions of graded algebras

: This study considers a class of doubly transitive groups satisfying the condition that the identity is the only element leaving three distinct letters fixed. The main object of the investigation is to classify the groups which do not contain a regular normal subgroup of order 1 + N in case N is even. (Author)

On a class of doubly transitive groups

Une théorie combinatoire des séries formelles

In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced. Of course, the solution will have a considerable effect on many related areas, both within group theory and outside. The purpose of this article is to consider the theory of finite permutation groups with the assumption that the finite simple groups are known, and to examine questions such as: which problems are solved or solvable under this assumption, and what important problems remain?

Finite permutation groups and finite simple groups

Preface to the second edition Preface to the first edition 1. On permutations 2. The definition of a group 3. On the simpler properties of a group which are independent of its mode of representation 4. Further properties of a group which are independent of its mode of representation 5. On the composition-series of a group 6. On the isomorphism of a group within itself 7. On Abelian groups 8. On groups whose orders are the powers of primes 9. On Sylow's theorem 10. On permutation-groups: transitive and intransitive groups 11. On permutation-groups: transitivity and primitivity 12. On the representation of a group of finite order as a permutation-group 13. On groups of linear substitutions 14. On the representation of a group of finite order as a group of linear substitutions 15. On group-characteristics 16. Some applications of the theory of groups of linear substitutions and of group-characteristics 17. On the invariants of groups of linear substitutions 18. On the graphical representation of a group 19. On the graphical representation of groups 20. On congruence groups Notes Index of technical terms Index of authors quoted General index.

/pdf/theory-of-groups-of-finite-order-112c4e67bh.pdf

Theory of Groups of Finite Order

The theory of equations

An Introduction to the Theory of Groups of Finite Order

A NOTICE of the “Treatise on the Theory of Functions,” by Profs. Harkness and Morley, appeared in NATURE during 1894 (vol. xlix. p. 477). The object of that work, as of Prof. Forsyth's book on the same subject, was to present a complete view of the theory as a whole, and to follow out its various developments as far as space permitted. It would not be correct to regard either of them as written for a student who could be fairly described as a beginner. What Prof. Klein somewhere calls “a certain ripeness of mathematical judgment,” which is just what a beginner does not possess, would be necessary in a reader who, without previous knowledge of the subject, could study such volumes with profit. Introduction to the Theory of Analytic Functions. By J. Harkness F. Morley Pp. xv + 336. (London: Macmillan and Co., Ltd., 1898.)

William Snow Burnside

Papers

Theory of Groups of Finite Order

The theory of equations

An Introduction to the Theory of Groups of Finite Order

Introduction to the Theory of Analytic Functions