Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-16T17:30:37.739Z Has data issue: false hasContentIssue false

Numbers of conjugacy classes in some finite classical groups

Published online by Cambridge University Press:  17 April 2009

I.G. Macdonald
Affiliation:
Department of Pure Mathematics, Queen Mary College, University of London, Mile End Road, London EI4NS, England.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we calculate the number of congugacy classes in the following finite classical groups: GLn(Fq); PGLn(Fq), SLn(Fq), and more generally G(Fq), where G is any algebraic group isogenous to SLn; PSLn(Fq); ; , , and more generally where G is any group isogenous to SUn over Fq; and .

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Feit, Walter and Fine, N.J., “Pairs of commuting matrices over a finite field”, Duke Math. J. 27 (1960), 9194.CrossRefGoogle Scholar
[2]Lehrer, G.I., “Characters, classes, and duality in isogenous groups”, J. Algebra 36 (1975), 278286.CrossRefGoogle Scholar
[3]Macdonald, I.G., “Zeta functions attached to finite general linear groups”, Math. Arm. 249 (1980), 115.Google Scholar
[4]Springer, T.A. and Steinberg, R., “Conjugacy classes”, Seminar on algebraic groups and related finite groups, Princeton, 1968/69, 167226 (Lecture Notes in Mathematics, 131. Springer-Verlag, Berlin, Heidelberg, New York, 1970).CrossRefGoogle Scholar
[5]Steinberg, Robert, Endomorphisms of linear algebraic groups (Memoirs of the American Mathematical Society, 80. American Mathematical Society, Providence, Rhode Island, 1968).Google Scholar
[6]Wall, G.E., “On the conjugacy classes in the unitary, symplectic and orthogonal groups”, J. Austral. Math. Soc. 3 (1963), 162.CrossRefGoogle Scholar
[7]Wall, G.E., “Conjugacy classes in projective and special linear groups”, Bull. Austral. Math. Soc. 22 (1980), 339364.CrossRefGoogle Scholar