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Journal of the London Mathematical Society 2002 66(3):605-622; doi:10.1112/S0024610702003678
© 2002 by London Mathematical Society
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© The London Mathematical Society

Cyclic, Separable and Semisimple Matrices in the Special Linear Groups Over a Finite Field

John R. Britnell

Mathematical Institute, University of Oxford 24–29 St Giles’, Oxford OX1 3LB

Received 21 May 2001. Revision received 21 March 2002.

A matrix A with minimum polynomial mA and characteristic polynomial cA is said to be cyclic if mA = cA, semisimple if mA has no repeated factors, and separable if it is both cyclic and semisimple. For any set T of matrices, we write CT for the proportion of cyclic matrices in T, SST for the proportion of semisimple matrices, and ST for the proportion of separable matrices. We will write CGL({infty},q) for limd->{infty}CGL(d,q), and so on.


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