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Counting cyclic and separable matrices over a finite field

Published online by Cambridge University Press:  17 April 2009

G.E. Wall
G.E. Wall
Affiliation:
School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia
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A square matrix is called cyclic if its characteristic and minimum polynomials coincide, separable if the characteristic polynomial has no repeated roots. Recent results of P. Neumann and Praeger, and of Lehrer, about the numbers of such matrices over a finite field are sharpened.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 2 , October 1999 , pp. 253 - 284
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Lehrer, G.I., ‘The cohomology of the regular semisimple variety’, J. Algebra 199 (1998), 666–689.CrossRefGoogle Scholar
[2]Lehrer, G.I. and Segal, G.B., ‘Homology stability for classical regular semisimple varieties’, (Report 98–27 (September 1998), School of Mathematics and Statistics, University of Sydney).Google Scholar
[3]Neumann, P.M. and Praeger, C.E., ‘Cyclic matrices over finite fields’, J. London Math. Soc. (2) 52 (1995), 263–284.Google Scholar