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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
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.
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- 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
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