Cycle indices for the finite classical groups

Details Cycle indices for the finite classical groups Cycle indices for the finite classical groups

1997-12-09

arxiv.org/abs/math/9712239v1

Mathematics

Group Theory

35 pages

Scientific paper

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.

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