When Abelian Groups Split

Authors

Rachel M. Thomas, Swarthmore CollegeFollow
Robert C. Rhoades, Bucknell University

Document Type

Article

Publication Date

8-1-2003

First Advisor

S. Allen Broughton

Abstract

Let S be a hyperbolic surface tiled by kaleidoscopic triangles. Let R_e denote the set of fixed points by the reflection in an edge, e, of a triangle. We say that R_e is separating if S-R_e has two components. Once we have a tiling, we can define a group of orientation preserving transformations, G. We develop a method for determining when a reflection is separating using the group algebra of G. Using this method we give necessary and sufficient conditions for a mirror to be separating when G is abelian. We also conjecture, that when G is simple there are no separating mirrors.

Comments

MSTR 03-01

Recommended Citation

Thomas, Rachel M. and Rhoades, Robert C., "When Abelian Groups Split" (2003). Mathematical Sciences Technical Reports (MSTR). 46.
https://scholar.rose-hulman.edu/math_mstr/46