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
| dc.contributor.author | Zhang, Qingxiang | |
| dc.date.accessioned | 2018-05-08T03:22:10Z | |
| dc.date.available | 2018-05-08T03:22:10Z | |
| dc.date.issued | 2006 | |
| dc.description.abstract | Let 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. | en_US |
| dc.identifier.uri | http://hdl.handle.net/10179/13334 | |
| dc.language.iso | en | en_US |
| dc.publisher | Massey University | en_US |
| dc.rights | The Author | en_US |
| dc.subject | Discrete geometry | en_US |
| dc.subject | Group theory | en_US |
| dc.subject | Generators | en_US |
| dc.title | 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 | en_US |
| dc.type | Thesis | en_US |
| massey.contributor.author | Zhang, Qingxiang | |
| thesis.degree.discipline | Mathematics | en_US |
| thesis.degree.grantor | Massey University | en_US |
| thesis.degree.level | Masters | en_US |
| thesis.degree.name | Master of Science (M. Sc.) | en_US |
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