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A Generating Function Approach to the Enumeration of Matrices in Classical Groups over Finite Fields
Jason Fulman, University of Pittsburgh, PA, Peter M. Neumann, Queen's College, Oxford, England, and Cheryl E. Praeger, University of Western Australia, Crawley, Australia
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Memoirs of the American Mathematical Society
2005; 90 pp; softcover
Volume: 176
ISBN-10: 0-8218-3706-0
ISBN-13: 978-0-8218-3706-1
List Price: US$62 Individual Members: US$37.20
Institutional Members: US\$49.60
Order Code: MEMO/176/830

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.

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