Matrix Generators for the Orthogonal Groups


L. J. Rylands and D. E. Taylor


Research Report 97-7
To appear in J. Symbolic Computation
Date: revised 5 March 1997


We describe the (well known) connection between the orthogonal groups over a finite field and the Chevalley groups of type Bm, Dm and 2Dm and their Lie algebras, then give matrix generators for the derived groups of the orthogonal groups. The generators correspond to Steinberg's generators for the associated Chevalley group. These generators allow the straightforward construction of the orthogonal groups in computer algebra systems such as Magma and GAP.

Key phrases

Matrix generators, orthogonal groups, Magma, symbolic computation

AMS Subject Classification (1991)

Primary: 68Q40
Secondary: 20G40, 20-04


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