Date of Award
Symmetric spaces of Lie groups and Riemannian manifolds have been an area of study since the seminal work of Cartan in the early 19th century with applications to representation theory, geometry, and number theory. Though originally defined in terms of Lie groups, the idea of a symmetry space has been generalized to finite groups as well, opening up a new field of research. In this thesis we find the generalized symmetric spaces of the modular group Mm(2). We begin by determining the structure of Mm(2). We then establish the automorphism group of Mm(2) and determine which of these auto-morphisms are involutions. Given an involution, Ø, we determine the fixed-point group, the generalized symmetric space and the extended symmetric space. This work completes the categorization of generalized symmetric spaces for the class of non-Abelian 2-groups which contain a cyclic subgroup of index 2.
Besson, Marc Julien, "Generalized Symmetric Spaces of the Modular Group Mm(2)" (2015). Dickinson College Honors Theses. Paper 190.