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A Generating Function Approach to the Enumeration of Matrices in Classical Groups over Finite Fields

Jason Fulman University of Pittsburgh, Pittsburgh, PA
Peter M. Neumann Queen’s College, Oxford, England
Cheryl E. Praeger University of Western Australia, Crawley, Australia
Available Formats:
Electronic ISBN: 978-1-4704-0431-4
Product Code: MEMO/176/830.E
List Price: $66.00 MAA Member Price:$59.40
AMS Member Price: $39.60 Click above image for expanded view A Generating Function Approach to the Enumeration of Matrices in Classical Groups over Finite Fields Jason Fulman University of Pittsburgh, Pittsburgh, PA Peter M. Neumann Queen’s College, Oxford, England Cheryl E. Praeger University of Western Australia, Crawley, Australia Available Formats:  Electronic ISBN: 978-1-4704-0431-4 Product Code: MEMO/176/830.E  List Price:$66.00 MAA Member Price: $59.40 AMS Member Price:$39.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1762005; 90 pp
MSC: Primary 05; Secondary 20;

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.

• Chapters
• 1. Introduction, tables, and preliminaries
• 2. Separable and cyclic matrices in classical groups
• 3. Semisimple and regular matrices in classical groups
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Volume: 1762005; 90 pp
MSC: Primary 05; Secondary 20;

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.

• Chapters
• 1. Introduction, tables, and preliminaries
• 2. Separable and cyclic matrices in classical groups
• 3. Semisimple and regular matrices in classical groups
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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