Linear characters of finite groups can be extended to take k operands. The basics of such a k-fold extension are detailed. We then examine a proposition by Johnson and Sehgal pertaining to these k-characters and disprove its converse. Probabilistic models can be applied to random walks on the Cayley groups of finite order. We examine random walks on dihedral groups which converge after a finite number of steps to the random walk induced by the uniform distribution. We present both sufficient and necessary conditions for such convergence and analyze aspects of algebraic geometry related to this subject.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Reese, Randall Dean, "Topics Pertaining to the Group Matrix: k-Characters and Random Walks" (2015). All Theses and Dissertations. 5570.
k-characters, group determinant, random walks, branched covering