Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
For each finitely generated subgroup of a Coxeter group, we define a cell complex called a completion. We show that these completions characterizes the index and normality of the subgroup. We construct a completion corresponding to the intersection of two subgroups and use this construction to characterize malnormality of subgroups of right-angled Coxeter groups. Finally, we show that if a completion of a subgroup is finite, then the subgroup is quasiconvex. Using this, we show that certain reflection subgroups of a Coxeter are quasiconvex.
Date
4-4-2024
Recommended Citation
Murphy, Jake A., "Subroups of Coxeter Groups and Stallings Foldings" (2024). LSU Doctoral Dissertations. 6423.
https://repository.lsu.edu/gradschool_dissertations/6423
Committee Chair
Dani, Pallavi