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On groups generated by three-dimensional special unitary groups II

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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We shall determine in this paper groups of types Dn, E6, E7 and E8 generated by SU(3, q)'s, q odd, q > 3. These groups are defined in Phan (1975). [We shall refer to this paper as I]. Acquaintance with the results of I is assumed. The identification of groups of type D4 is similar to that of SU(n, q). We actually construct an isomorphism from the universal group of type D4 onto Spin+(8, q). This direct approach does not appear to be feasible for groups of type Dn with n ≧ 5. Fortunately Wong's recent result (1974) is applicable here. But his theorem requires that the characteristic of the field be odd; hence unlike the unitary case, we assume that q is odd and q 3. Using Wong's theorem, we proceed to show by induction that groups of type Dn are homomorphic images of Spin+(2n, q) or Spin −(2n, q) according as n is even or n is odd.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 2 , March 1977 , pp. 129 - 146
Copyright
Copyright © Australian Mathematical Society 1977

References

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