Faithful Blockings of Finite Groups and Pedagogical Applications
Open Access
Author:
Medwid, Mark Edward
Area of Honors:
Mathematics (Behrend)
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
Paul Becker, Thesis Supervisor Joseph Peter Previte, Thesis Honors Advisor
Keywords:
algebra abstract algebra group theory representation theory linear algebra advanced mathematics
Abstract:
The thesis research project was in two areas: abstract algebra and pedagogy. Specifically, we explored which groups can be represented by blocked permutation matrices (called faithful blockings); we then used these representations to enhance teaching in abstract algebra and related courses. These faithful blockings offer a concrete picture of an abstract subject. The main pedagogical focus was the development of computer lab supplements for upper-level mathematics courses at Behrend. Our project had the following results: a new algebra theorem – every symmetric group admits a faithful blocking by non-normal subgroups; a new definition, “relatively normal” subgroups; some new results that brought about new examples of matrix representations for groups, and the development of the above mentioned computer labs. These results were presented by Dr. Becker at an AMS special session on Undergraduate Education: A Vision for the 21st Century (Notre Dame University, Nov. 2010).
