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The Character Tables for SL(3, q), SU(3, q2), PSL(3, q), PSU(3, q2)

Published online by Cambridge University Press:  20 November 2018

William A. Simpson  and
J. Sutherland Frame
William A. Simpson
Affiliation:
Michigan State University, East Lansing, Michigan
J. Sutherland Frame
Affiliation:
Michigan State University, East Lansing, Michigan
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In this paper the character table of GL(3, q) (U(3, q2)), the group of all nonsingular n × n (unitary) matrices over GF(q) (GF(q2)), is used to obtain the character tables for the related subgroups SL(3, q), PSL(3, q) (SU(3, q2), PSU(3, q2)), the corresponding groups of matrices of determinant unity and the projective group respectively. There are very few abstract character tables which hold for entire families of groups. Such tables are of much greater value than tables for specific groups because, among other things, they enable one to discern various patterns common to the whole family.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 3 , June 1973 , pp. 486 - 494
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Dickson, L. E., Linear groups (Dover, New York, 1958).Google Scholar
2. Ennola, V., Characters of finite unitary groups, Ann. Acad. Sci. Fenn. Ser. A, I. 323 (1963), 120–55.Google Scholar
3. Ennola, V., Conjugacy classes of the finite unitary groups, Ann. Acad. Sci. Fenn. Ser. A, 1. 313 (1962), 1–12.Google Scholar
4. Gorenstein, D., Finite groups (Harper and Row, New York, 1968).Google Scholar
5. Green, J. A., Characters of the finite general linear groups, Trans. Amer. Math. Soc. 80 (1955), 407–77.Google Scholar
6. Jordan, H. E., Characteristics of various linear groups, Amer. J. Math. 39 (1907), 387–405.Google Scholar
7. Schur, I., Untersuchungen Uber Die Darstellung Der Endlichen Gruppen Durch Gebrochene Lineare Substitutionen, J. Reine Angew. Math. 132 (1907), 85–137.Google Scholar
8. Steinberg, R., The Representations of GL(3, q)t GL(4, q), PGL(3, q), and PGL(4, q), Can. J. Math. 3 (1951), 225–35.Google Scholar
9. Wall, G. E., The conjugacy classes of classical groups, J. Austral. Math. Soc. 3 (1965), 1–62.Google Scholar