Linear groups 线性群

Hailed as a milestone in the development of modern algebra, this classic exposi-tion 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 mathe-matics. 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 nega-tive curvature, respectively), can be completely characterized by groups.
Linear Groups is divided into two parts. The first contains an extensive and thor-ough presentation of the theory of Galois Fields and is especially valuable for its enormous wealth of examples and theorems. The second part features a com-prehensive discussion of linear groups in a Galois Field and contains a survey of the known simple groups of finite composite order. The author provides com-prehensive detail about each group, much of which cannot easily be found else-where.

FIRST PART INTRODUCTION TO THE GALOIS FIELD THEORY
CHAPTER I.Definition and properties of finite fields
CHAPTER II.Proof of the existence of the GF(pm)for every prime p and integer m.
CHAPTER III.Classification and determination of irreducible quantics
CHAPTER IV.Miscellaneous properties of Galois Fields
CHAPTER V.Analytic representation of substitutions on the marks of a Galois Field
SECOND PART.THEORY OF LINEAR GROUPS IN A GALOIS FIELD
CHAPTER I.General linear homogeneous group
CHAPTER II.The Abelian linear group
CHAPTER III.A generalization of the Abelian linear group
CHAPTER IV.The hyperabelian group
CHAPTER V.The hyperorthogonal and related linear groups
CHAPTER VI.The compounds of a linear homogeneous group
CHAPTER VII.Linear homogeneous group in the GF(pn),p>2,defined by a quadratic invariant
CHAPTER VIII.Linear homogeneous group in the GB(2n)defined by a quadratic invariant
CHAPTER IX.Linear groups with certain invariants of degree q>2.
CHAPTER X.Canonical form and classification of linear substitutions
CHAPTER XI.Operators and cyclic subgroups of the simple group
CHAPTER XII.Subgroups of the linear fractional group LF(2,pn)
CHAPTER XIII.Auxiliary theorems on abstract groups.Abstract forms of various linear groups.
CHAPTER XIV.Group of the equation for the 27 straight lines on a general surface of the third order
CHAPTER XV.Summary of the known systems of simple groups
INDEX OF SUBJECTS