Abstract

This thesis presents an introduction to Schur rings (S-rings) and their various properties. Special attention is given to S-rings that are commutative. A number of original results are proved, including a complete classification of the central S-rings over the simple groups PSL(2,q), where q is any prime power. A discussion is made of the counting of symmetric S-rings over cyclic groups of prime power order. An appendix is included that gives all S-rings over the symmetric group over 4 elements with basic structural properties, along with code that can be used, for groups of comparatively small order, to enumerate all S-rings and compute character tables for those S-rings that are commutative. The appendix also includes code optimized for the enumeration of S-rings over cyclic groups.

Degree

MS

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2016-06-01

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd8771

Keywords

Schur rings, association schemes, algebraic combinatorics, projective special linear groups

Included in

Mathematics Commons

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