Modular Reduction of the Tail-Triangle Coxeter Groups Gamma = [5,K;L] With K,L E {3, 4, 6}
Date of Award
5-2022
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
First Advisor
Ma. Louise Antonette N. De Las Peñas, PhDMark L. Loyola, PhD
Abstract
This study discusses the modular reduction method with moduli given by primes in the quadratic integer ring Z[⌧ ], where ⌧ = 1+p52 , to construct finite tail-triangle C-groups. The method is adapted from the modular reduction technique for abstract polytopes given in Monson and Schulte’s work (Monson and Schulte, 2009) and applied to a rank 4 tail-triangle Coxeter group = [5, k; l] with k,l 2 {3, 4, 6}. A description of the constructed tail-triangle C-groups and their distinguished 3-generator subgroups as the orthogonal group O(n, q, ") or O1(n, q, "); or the reduction modulo a prime p of one of the finite irreducible Coxeter groups A3, A4, B3, B4, D4, F4, H3 or H4 is also presented.
Key Words: modular reduction, tail-triangle C-groups, tail-triangle Coxeter groups
Recommended Citation
Nonie Elvin, Leyrita S., (2022). Modular Reduction of the Tail-Triangle Coxeter Groups Gamma = [5,K;L] With K,L E {3, 4, 6}. Archīum.ATENEO.
https://archium.ateneo.edu/theses-dissertations/759
