Article contents
On groups generated by three-dimensional special unitary groups II
Published online by Cambridge University Press: 09 April 2009
Extract
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
- Copyright
- Copyright © Australian Mathematical Society 1977
References
- 12
- Cited by