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Some subgroups of SL(3, z) generated by involutions

Published online by Cambridge University Press:  18 May 2009

Stephen P. Humphries
Stephen P. Humphries
Affiliation:
Department of MathematicsBrigham Young UniversityProvoUtah 84602, U.S.A.
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For R a commutative ring with identity 1 we let SL(n, R) denote the group of n × n integral matrices with determinant 1. A transvection T is an element of SL(n, R) which we represent (see [1]) as a pair (φ d) where φ ∈ (Rn)*, the dual space of Rn, d ∈ Rn, φ(d) = 0, and for all x ∈ Rn we have

T(x) = + φ(x) d.

Throughout this paper an involution is an element Y of SL(n, R) which has order two. Let n = 3 and R = Z and let C = diag(–1, –1, –1) be the central element of GL(3, Z).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 2 , May 1990 , pp. 127 - 136
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

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