Parameters of the two generator discrete elementary groups : a thesis presented in partial fulfillment of the requirements for the degree of Master of Science in Mathematics at Massey University, Albany, New Zealand

Zhang, Qingxiang2018-05-082018-05-082006http://hdl.handle.net/10179/13334Let f, g be elements of M, the group of Möbius transformations of the extended complex plane Ĉ = C U ∞. We identify each element of M with a 2 × 2 complex matrix with determinant 1. The three complex numbers, β(f) = tr2 (f) - 4,β(g) = tr2 (g) - 4,γ(f,g) = tr[f,g] - 2, define the group ‹f,g› uniquely up to conjugacy whenever γ(f,g) ≠ 0; where tr(f) and tr(g) denote the traces of representive matrices of f and g respectively, [f,g] denotes the multiplicative commutator fgf-1 g-1 . We call these three complex numbers the parameters of ‹f,g›. This thesis is concerned with the parameters of discrete and elementary subgroups of M.enThe AuthorDiscrete geometryGroup theoryGeneratorsParameters of the two generator discrete elementary groups : a thesis presented in partial fulfillment of the requirements for the degree of Master of Science in Mathematics at Massey University, Albany, New ZealandThesisQ112236888https://www.wikidata.org/wiki/Q112236888