Cycle indices for the finite classical groups
- 1 January 1999
- journal article
- research article
- Published by Walter de Gruyter GmbH in Journal of Group Theory
- Vol. 2 (3) , 251-289
- https://doi.org/10.1515/jgth.1999.017
Abstract
This paper defines and develops cycle indices for the finite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include semisimplicity, regularity, regular semisimplicity, the characteristic polynomial, number of Jordan blocks, and average order of a matrix.Keywords
This publication has 20 references indexed in Scilit:
- The Cohomology of the Regular Semisimple VarietyJournal of Algebra, 1998
- Cyclic Matrices Over Finite FieldsJournal of the London Mathematical Society, 1995
- How random is the characteristic polynomial of a random matrix ?Mathematical Proceedings of the Cambridge Philosophical Society, 1993
- The Number of Regular Semisimple Elements for Chevalley Groups of Classical TypeJournal of Algebra, 1993
- Rational tori, semisimple orbits and the topology of hyperplane complementsCommentarii Mathematici Helvetici, 1992
- A central limit theorem on gln(fq)Random Structures & Algorithms, 1991
- The Expected order of a Random PermutationBulletin of the London Mathematical Society, 1991
- The cycle structure of a linear transformation over a finite fieldLinear Algebra and its Applications, 1981
- On the Foundations of Combinatorial Theory IV Finite Vector Spaces and Eulerian Generating FunctionsStudies in Applied Mathematics, 1970
- Ordered cycle lengths in a random permutationTransactions of the American Mathematical Society, 1966