Mathematics Research Seminar Series: Modular Reduction of the Star Coxeter Group [5,3;3]

Mathematics Research Seminar Series
Modular Reduction of the Star Coxeter Group [5,3;3]

by Nonie Elvin S. Leyrita,
Father Saturnino Urios University

Date: Wednesday, 09 November 2022
Time: 4:00 pm
Venue: https://bit.ly/AdmuMathSeminar

In this talk, we are going to discuss the application of the modular reduction technique to the star Coxeter group G=[5,3;3]. As moduli, we use the primes p in a certain quadratic integer ring. We prove that the reduced group is a C-group regardless of the prime used in the reduction. Thus, this group is the automorphism group of an alternating semiregular 4-polytope of type {5,3;3}. Furthermore, we classify the obtained C-groups and their distinguished 3-generator subgroups as orthogonal groups over finite fields or as modular reductions of certain irreducible Coxeter groups. At the end of the talk, we shall also state analogous results for more general cases.