Publisher's Synopsis
This monograph provides a survey of classical groups over finite fields. Many important results, appearing for the first time in book-form, are clearly presented. Most of them have been obtained by the author and students under his supervision.;The book should prove a useful reference for those who work on classical groups, finite fields, finite geometry, combinatorics, block designs and coding theory. Only a basic knowledge of abstract and linear algebra is required.;The first two chapters are on affine geometry and projective geometry. These chapters contain new results and new derivations of old results. Chapters 3 to 7, the main contents of the book, treat the geometry of symplectic, pseudo-symplectic, unitary and orthogonal groups over finite fields. Connections with polar spaces and generalized quadrangles are pointed out, and applications to error-correcting codes, authentication codes and projective codes are given as examples or exercises.;Exercises are provided at the end of each chapter.
