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Some subgroups of SL(3, z) generated by involutions
Published online by Cambridge University Press: 18 May 2009
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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).
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- Copyright © Glasgow Mathematical Journal Trust 1990
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