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On groups generated by three-dimensional special unitary groups I

Published online by Cambridge University Press:  09 April 2009

Kok-Wee Phan
Kok-Wee Phan
Affiliation:
Department of Mathematics University of Notre Dame Notre Dame, U.S.A.
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This paper is the result of our attempt to carry over the method of our characterization of the linear groups PSL(n, q) (Phan (1972)) to that of the unitary groups PSU (n, q). It appears desirable to have available a result on the generation of the unitary groups more closely related to the splitting of the underlying hermitian spaces of these groups into orthogonal direct sum of anisotropic lines. Another motivation comes also from our work on the unitary groups in which we obtained a fusion pattern different from that of the unitary group when the dimension of the underlying space is eight. This fusion pattern produces a group whose structure is not immediately apparent. In order to identify this group, the result of this paper appears to be a necessary step.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1977 , pp. 67 - 77
Copyright
Copyright © Australian Mathematical Society 1977

References

Dieudonxné, Jean (1955), La Géométrie des Groupes Classiques (Ergebnisse der Mathematik und ihrer Grenzgebiete, 5. Springer-Verlag, Berlin, Göttingen, Heidelberg, 1955).Google Scholar
Phan, Kok-Wee (1972), ‘A characterization of the finite groupsPSL(n, q)’, Math. Z. 124, 169–185.CrossRefGoogle Scholar
Springer, T. A. and Steinberg, R. (1970), ‘Conjugacy classes’, Seminar on Algebraic Groups and Related Finite Groups, EI–E100 (Lecture Notes in Mathematics, 131. Springer-Verlag, Berlin, Heidelberg, New York, 1970).Google Scholar