Linear Groups with an Exposition of Galois Field Theory

Abstract

Hailed as a milestone in the development of modern algebra, this classic exposition of the theory of groups was written by a distinguished mathematician who has made significant contributions to the field of abstract algebra. The text is well within the range of graduate students and of particular value in its attention to practical applications of group theory - applications that have given this formerly obscure area of investigation a central place in pure mathematics. These applications include the theory of the solvability of equations, theory of differential equations, complex number systems, and - preeminently - the foundations of geometry, where Euclidean or parabolic geometry, elliptic geometry, and hyperbolic geometry (corresponding to zero, positive, or negative curvature, respectively), can be completely characterized by groups. Linear Groups is divided into two parts. The first contains an extensive and thorough presentation of the theory of Galois Fields and is especially valuable for its enormous wealth of examples and theorems. The second part features a comprehensive discussion of linear groups in a Galois Field and contains a survey of the known simple groups of finite composite order. The author provides comprehensive detail about each group, much of which cannot easily be found elsewhere.