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

Share

COinS