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Non-Hurwitz Classical Groups

Published online by Cambridge University Press:  01 February 2010

R. Vincent  and
A.E. Zalesski
R. Vincent
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR47TJ, United Kingdom, Robert.Vincent@uea.ac.uk
A.E. Zalesski
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR47TJ, United Kingdom, a.zalesskii@uea.ac.uk

Abstract

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In previous work by Di Martino, Tamburini and Zalesski [Comm. Algebra 28 (2000) 5383–5404] it is shown that certain low-dimensional classical groups over finite fields are not Hurwitz. In this paper the list is extended by adding the special linear and special unitary groups in dimensions 8.9,11.13. We also show that all groups Sp(n, q) are not Hurwitz for q even and n = 6,8,12,16. In the range 11 < n < 32 many of these groups are shown to be non-Hurwitz. In addition, we observe that PSp(6, 3), PΩ±(8, 3k), PΩ±10k), Ω(11,3k), Ω±(14,3k), Ω±(16,7k), Ω(n, 7k) for n = 9,11,13, PSp(8, 7k) are not Hurwitz.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 10 , 2007 , pp. 21 - 82
Copyright
Copyright © London Mathematical Society 2007

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