# Matrix Generators for the Orthogonal Groups

## Author

**L. J. Rylands** and **D. E. Taylor**

## Status

Research Report 97-7

To appear in J. Symbolic Computation

Date: revised 5 March 1997

## Abstract

We describe the (well known) connection between the orthogonal groups
over a finite field and the Chevalley groups of type `B`_{m},
`D`_{m} and ^{2}`D`_{m} 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

## Content

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1997-7.dvi (47kB)

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Sydney Mathematics and Statistics