{"id":{"repo_id":"mo-state","oai_identifier":"oai:bearworks.missouristate.edu:theses-1855"},"canonical_url":"https://search.dev.ndltd.org/etd/mo-state/oai:bearworks.missouristate.edu:theses-1855","repository":{"repo_id":"mo-state","name":"Missouri State University","base_url":"https://bearworks.missouristate.edu/do/oai/"},"display":{"title":"On Proofs of Sylow's Theorem","abstract":"We give five proofs of Sylow's Theorem. The proofs given will be Sylow's original proof, the Cauchy-Frobenius proof using double cosets, Frobenius' proof (two versions) using the class equation, and Wielandt's proof using subsets. We give a number of different examples to illustrate the various proofs. We put Sylow's work in historical context. We give an application of Sylow's Theorem in the proof of the Fundamental Theorem of Algebra. We give a determination of conjugacy classes in the Dihedral group. We conclude with a sketch of Sylow.","abstract_html":"We give five proofs of Sylow's Theorem. The proofs given will be Sylow's original proof, the Cauchy-Frobenius proof using double cosets, Frobenius' proof (two versions) using the class equation, and Wielandt's proof using subsets. We give a number of different examples to illustrate the various proofs. We put Sylow's work in historical context. We give an application of Sylow's Theorem in the proof of the Fundamental Theorem of Algebra. We give a determination of conjugacy classes in the Dihedral group. We conclude with a sketch of Sylow.","abstract_has_math":false,"creators":["Marshall, Lucille"],"institution":null,"degree_name":"Master of Science in Mathematics","degree_level":"Masters","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Kishor Shah"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2000,"date_issued":"2000-07-01T07:00:00Z","date_published":"2000-07-01T07:00:00Z","updated_at":"2026-07-24T03:15:54Z","subjects":["Mathematics"],"languages":[],"rights":["© Lucille Marshall"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://bearworks.missouristate.edu/theses/854","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kishor Shah"]},{"key":"dc:creator","label":"Author","values":["Marshall, Lucille"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["© Lucille Marshall"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://bearworks.missouristate.edu/theses/854"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We give five proofs of Sylow's Theorem. The proofs given will be Sylow's original proof, the Cauchy-Frobenius proof using double cosets, Frobenius' proof (two versions) using the class equation, and Wielandt's proof using subsets. We give a number of different examples to illustrate the various proofs. We put Sylow's work in historical context. We give an application of Sylow's Theorem in the proof of the Fundamental Theorem of Algebra. We give a determination of conjugacy classes in the Dihedral group. We conclude with a sketch of Sylow."]},{"key":"dc:title","label":"Title","values":["On Proofs of Sylow's Theorem"]}]}],"canonical_facts":{"dc:contributor":["Kishor Shah"],"dc:creator":["Marshall, Lucille"],"dc:description.abstract":["We give five proofs of Sylow's Theorem. The proofs given will be Sylow's original proof, the Cauchy-Frobenius proof using double cosets, Frobenius' proof (two versions) using the class equation, and Wielandt's proof using subsets. We give a number of different examples to illustrate the various proofs. We put Sylow's work in historical context. We give an application of Sylow's Theorem in the proof of the Fundamental Theorem of Algebra. We give a determination of conjugacy classes in the Dihedral group. We conclude with a sketch of Sylow."],"dc:identifier":["https://bearworks.missouristate.edu/theses/854"],"dc:rights":["© Lucille Marshall"],"dc:subject":["Mathematics"],"dc:title":["On Proofs of Sylow's Theorem"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Masters"],"thesis:degree_name":["Master of Science in Mathematics"]},"updated_at":"2026-07-24T03:15:54Z"}