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A theorem on power series with applications to classical groups over finite fields

Published online by Cambridge University Press:  17 April 2009

Andrew J. Spencer
Andrew J. Spencer
Affiliation:
St. Hugh's College, Oxford OX2 6LE, United Kingdom
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Abstract

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For some of the classical groups over finite fields it is possible to express the proportion of eigenvalue-free matrices in terms of generating functions. We prove a theorem on the monotonicity of the coefficients of powers of power series and apply this to the generating functions of the general linear, symplectic and orthogonal groups. This proves a conjecture on the monotonicity of the proportions of eigenvalue-free elements in these groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 121 - 129
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Neumann, P.M. and Praeger, C.E., ‘Derangements and eigenvalue-free elements in finite classical groups’, J. London Math. Soc. (2) 58 (1998), 564–586.CrossRefGoogle Scholar