Generating function techniques are used to study the probability that an element of a classical group defined over a finite field is separable, cyclic, semisimple or regular. The limits of these probabilities as the dimension tends to infinity are calculated in all cases, and exponential convergence to the limit is proved. These results complement and extend earlier results of the authors, G. E. Wall, and Guralnick & Lübeck.

Table of Contents

• Introduction, tables, and preliminaries
• Separable and cyclic matrices in classical groups
• Semisimple and regular matrices in classical groups
• Bibliography