We investigate conditions under which the commutant of a Moufang loop is normal and related topics. We begin by giving relevant background on Moufang loops and normality. We then prove a theorem showing how close the commutant is to being normal: cR(x, y)R(x, y)R(x, y) = c. We then prove a couple of theorems emphasizing the importance of cubes in Moufang loops. Finally we prove a decomposition theorem for the multiplication group of a finite commutative Moufang loop.
","abstract_html":"<p>We investigate conditions under which the commutant of a Moufang loop is normal and related topics. We begin by giving relevant background on Moufang loops and normality. We then prove a theorem showing how close the commutant is to being normal: cR(x, y)R(x, y)R(x, y) = c. We then prove a couple of theorems emphasizing the importance of cubes in Moufang loops. Finally we prove a decomposition theorem for the multiplication group of a finite commutative Moufang loop.</p>","abstract_has_math":false,"creators":["Phillips, Evan"],"institution":null,"degree_name":"Master of Science","degree_level":"Thesis","degree_discipline":"Math and Computer Science","degree_department":null,"school":null,"contributors":["Dr. Daniel Rowe"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-11-01T07:00:00Z","date_published":"2024-11-01T07:00:00Z","updated_at":"2026-07-24T03:24:36Z","subjects":["Moufang","Loop","Commutant","Normal","Algebra"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.nmu.edu/theses/865","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. Daniel Rowe"]},{"key":"dc:creator","label":"Author","values":["Phillips, Evan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2024-11-15T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Math and Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Moufang","Loop","Commutant","Normal","Algebra"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.nmu.edu/theses/865"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We investigate conditions under which the commutant of a Moufang loop is normal and related topics. We begin by giving relevant background on Moufang loops and normality. We then prove a theorem showing how close the commutant is to being normal: cR(x, y)R(x, y)R(x, y) = c. We then prove a couple of theorems emphasizing the importance of cubes in Moufang loops. Finally we prove a decomposition theorem for the multiplication group of a finite commutative Moufang loop.
"]},{"key":"dc:title","label":"Title","values":["The Near Normality of the Commutant of a Moufang Loop"]}]}],"canonical_facts":{"dc:contributor":["Dr. Daniel Rowe"],"dc:creator":["Phillips, Evan"],"dc:date.available":["2024-11-15T08:00:00Z"],"dc:description.abstract":["We investigate conditions under which the commutant of a Moufang loop is normal and related topics. We begin by giving relevant background on Moufang loops and normality. We then prove a theorem showing how close the commutant is to being normal: cR(x, y)R(x, y)R(x, y) = c. We then prove a couple of theorems emphasizing the importance of cubes in Moufang loops. Finally we prove a decomposition theorem for the multiplication group of a finite commutative Moufang loop.
"],"dc:identifier":["https://commons.nmu.edu/theses/865"],"dc:subject":["Moufang","Loop","Commutant","Normal","Algebra"],"dc:title":["The Near Normality of the Commutant of a Moufang Loop"],"thesis:degree_discipline":["Math and Computer Science"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T03:24:36Z"}