The McKay-Alperin-Dade Conjecture, which has not been finally verified, predicts the number of complex irreducible characters in various p-blocks of a finite group G as an alternating sum of the numbers of characters in related p-blocks of certain subgroups of G. The sub-groups involved are the normalizers of representatives of conjugacy classes of radical p-chains of G. For this reason, it is of interest to study radical p-chains. In this thesis, we examine the group L3(2) and determine representatives of the conjugacy classes of radical p-subgroups and radical p-chains for the primes p = 2, 3, and 7. We then determine the structure of the normalizers of these subgroups and chains.
","abstract_html":"<p>The McKay-Alperin-Dade Conjecture, which has not been finally verified, predicts the number of complex irreducible characters in various <em>p</em>-blocks of a finite group <em>G</em> as an alternating sum of the numbers of characters in related <em>p</em>-blocks of certain subgroups of <em>G</em>. The sub-groups involved are the normalizers of representatives of conjugacy classes of radical <em>p</em>-chains of <em>G</em>. For this reason, it is of interest to study radical <em>p</em>-chains. In this thesis, we examine the group L<sub>3</sub>(2) and determine representatives of the conjugacy classes of radical <em>p</em>-subgroups and radical <em>p</em>-chains for the primes <em>p</em> = 2, 3, and 7. We then determine the structure of the normalizers of these subgroups and chains.</p>","abstract_has_math":false,"creators":["Belcher, Donald Dewayne"],"institution":null,"degree_name":"MS (Master of Science)","degree_level":"Thesis - unrestricted","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2001,"date_issued":"2001-05-01T07:00:00Z","date_published":"2001-05-01T07:00:00Z","updated_at":"2026-07-24T02:19:07Z","subjects":["radical p-subgroups","group theory","mckay-alperin-dade conjecture","radical p-chains","Physical Sciences and Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/133","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Belcher, Donald Dewayne"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["1900-01-01T08:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2001-05-01T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - unrestricted"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS (Master of Science)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["radical p-subgroups","group theory","mckay-alperin-dade conjecture","radical p-chains","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright by the authors."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dc.etsu.edu/context/etd/article/1183/viewcontent/belcherd.pdf","https://dc.etsu.edu/etd/133"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The McKay-Alperin-Dade Conjecture, which has not been finally verified, predicts the number of complex irreducible characters in various p-blocks of a finite group G as an alternating sum of the numbers of characters in related p-blocks of certain subgroups of G. The sub-groups involved are the normalizers of representatives of conjugacy classes of radical p-chains of G. For this reason, it is of interest to study radical p-chains. In this thesis, we examine the group L3(2) and determine representatives of the conjugacy classes of radical p-subgroups and radical p-chains for the primes p = 2, 3, and 7. We then determine the structure of the normalizers of these subgroups and chains.
"]},{"key":"dc:title","label":"Title","values":["Radical p-chains in L3(2)."]}]}],"canonical_facts":{"dc:creator":["Belcher, Donald Dewayne"],"dc:date.available":["1900-01-01T08:00:00Z"],"dc:date.issued":["2001-05-01T07:00:00Z"],"dc:description.abstract":["The McKay-Alperin-Dade Conjecture, which has not been finally verified, predicts the number of complex irreducible characters in various p-blocks of a finite group G as an alternating sum of the numbers of characters in related p-blocks of certain subgroups of G. The sub-groups involved are the normalizers of representatives of conjugacy classes of radical p-chains of G. For this reason, it is of interest to study radical p-chains. In this thesis, we examine the group L3(2) and determine representatives of the conjugacy classes of radical p-subgroups and radical p-chains for the primes p = 2, 3, and 7. We then determine the structure of the normalizers of these subgroups and chains.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/1183/viewcontent/belcherd.pdf","https://dc.etsu.edu/etd/133"],"dc:rights":["Copyright by the authors."],"dc:subject":["radical p-subgroups","group theory","mckay-alperin-dade conjecture","radical p-chains","Physical Sciences and Mathematics"],"dc:title":["Radical p-chains in L3(2)."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:19:07Z"}