{"id":{"repo_id":"ohiolink","oai_identifier":"oai:etd.ohiolink.edu:akron1365259761"},"canonical_url":"https://search.dev.ndltd.org/etd/ohiolink/oai:etd.ohiolink.edu:akron1365259761","repository":{"repo_id":"ohiolink","name":"OhioLINK","base_url":"https://etd.ohiolink.edu/acprod/odb_etd/ws/oai/oai"},"display":{"title":"Orders of Perfect Groups with Dihedral Involution Centralizers","abstract":"Let G be a finite group that is equal to its commutator subgroup, and suppose that G contains an element of order 2 whose centralizer in G is dihedral of 2-power order. We study the cases where this centralizer is dihedral of order 8, 16, 32, 64, 128, or 256. It is true in each case that this centralizer is a Sylow 2-subgroup of G. We then use character-theoretic techniques to generate a list of possibilities for the order of G. In the process of generating this list of possible orders, we prove several results about the structure of our group under consideration. We then strengthen the original hypotheses to require G to be non-abelian simple, and we use the results proved about the structure of G to eliminate all possible orders such that there is no non-abelian simple group of that order.","abstract_html":"Let G be a finite group that is equal to its commutator subgroup, and suppose that G contains an element of order 2 whose centralizer in G is dihedral of 2-power order. We study the cases where this centralizer is dihedral of order 8, 16, 32, 64, 128, or 256. It is true in each case that this centralizer is a Sylow 2-subgroup of G. We then use character-theoretic techniques to generate a list of possibilities for the order of G. In the process of generating this list of possible orders, we prove several results about the structure of our group under consideration. We then strengthen the original hypotheses to require G to be non-abelian simple, and we use the results proved about the structure of G to eliminate all possible orders such that there is no non-abelian simple group of that order.","abstract_has_math":false,"creators":["Strayer, Michael Christopher"],"institution":"University of Akron","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Riedl, Jeffrey"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-05-23","date_published":"2013-05-23","updated_at":"2026-07-24T03:37:31Z","subjects":["Mathematics","simple groups","dihedral groups","involutions","projective special linear groups","character theory"],"languages":["English"],"rights":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://rave.ohiolink.edu/etdc/view?acc_num=akron1365259761","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Riedl, Jeffrey"]},{"key":"dc:creator","label":"Author","values":["Strayer, Michael Christopher"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-05-23"]},{"key":"dc:publisher","label":"Institution","values":["University of Akron / OhioLINK"]},{"key":"dc:type","label":"Dc Type","values":["Electronic Thesis or Dissertation"]},{"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"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Akron"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","simple groups","dihedral groups","involutions","projective special linear groups","character theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. 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We then strengthen the original hypotheses to require G to be non-abelian simple, and we use the results proved about the structure of G to eliminate all possible orders such that there is no non-abelian simple group of that order."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf","p.76","360.7 KB"]},{"key":"dc:title","label":"Title","values":["Orders of Perfect Groups with Dihedral Involution Centralizers"]}]}],"canonical_facts":{"dc:contributor":["Riedl, Jeffrey"],"dc:creator":["Strayer, Michael Christopher"],"dc:date":["2013-05-23"],"dc:description":["Let G be a finite group that is equal to its commutator subgroup, and suppose that G contains an element of order 2 whose centralizer in G is dihedral of 2-power order. We study the cases where this centralizer is dihedral of order 8, 16, 32, 64, 128, or 256. It is true in each case that this centralizer is a Sylow 2-subgroup of G. We then use character-theoretic techniques to generate a list of possibilities for the order of G. In the process of generating this list of possible orders, we prove several results about the structure of our group under consideration. We then strengthen the original hypotheses to require G to be non-abelian simple, and we use the results proved about the structure of G to eliminate all possible orders such that there is no non-abelian simple group of that order."],"dc:format":["application/pdf","p.76","360.7 KB"],"dc:identifier":["http://rave.ohiolink.edu/etdc/view?acc_num=akron1365259761"],"dc:language":["English"],"dc:publisher":["University of Akron / OhioLINK"],"dc:rights":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."],"dc:subject":["Mathematics","simple groups","dihedral groups","involutions","projective special linear groups","character theory"],"dc:title":["Orders of Perfect Groups with Dihedral Involution Centralizers"],"dc:type":["Electronic Thesis or Dissertation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["University of Akron"]},"updated_at":"2026-07-24T03:37:31Z"}