{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/72540"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/72540","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On P-Radical P-Blocks of Group Algebras","abstract":"p-Radical p-blocks of finite group algebras are studied. Much of the p-radical group theory is generalized to p-blocks through R. Knorr's work on simple induction and restriction pairs. In addition, several results concerning such blocks are proved.","abstract_html":"p-Radical p-blocks of finite group algebras are studied. Much of the p-radical group theory is generalized to p-blocks through R. Knorr's work on simple induction and restriction pairs. In addition, several results concerning such blocks are proved.","abstract_has_math":false,"creators":["Laradji, Abdellatif"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Suzuki, Michio"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-17T23:17:47Z","date_published":"2014-12-17T23:17:47Z","updated_at":"2026-07-22T22:26:07Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI9329091"],"render_values":[{"text":"(UMI)AAI9329091","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/72540","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Suzuki, Michio"]},{"key":"dc:creator","label":"Author","values":["Laradji, Abdellatif"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-17T23:17:47Z","10000-01-01","1993"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/72540","(UMI)AAI9329091"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["p-Radical p-blocks of finite group algebras are studied. Much of the p-radical group theory is generalized to p-blocks through R. Knorr's work on simple induction and restriction pairs. In addition, several results concerning such blocks are proved.","The most interesting fact known about p-radical groups is a result of T. Okuyama, who showed that such groups are p-solvable. It turns out that the same conclusion could be reached assuming much less. In fact, it is shown that finite groups, whose principal p-blocks are p-radical, are p-solvable. This is not in general true for non-principal blocks as illustrated by some examples. Nevertheless, in any case, simple modules in p-radical blocks behave somewhat like those in blocks of p-solvable groups.","A p-block, in which every (modular) simple module has vertices contained in the kernel, is characterized. Such a block enjoys a property much stronger than p-radicality. If, in addition, every simple module in this block has vertices conjugate to a defect group of the block, further characterizations are derived. As a consequence, some characterizations of p-length 1 p-solvable groups, in terms of the ordinary irreducible characters of the principal p-blocks, are given.","Made available in DSpace on 2014-12-17T23:17:47Z (GMT). No. of bitstreams: 1 9329091.pdf: 2515719 bytes, checksum: 59d3bc2a6181018bc344209affc81353 (MD5) Previous issue date: 1993","Embargo set by: Seth Robbins for item 72708 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","77 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1993."]},{"key":"dc:title","label":"Title","values":["On P-Radical P-Blocks of Group Algebras"]}]}],"canonical_facts":{"dc:contributor":["Suzuki, Michio"],"dc:creator":["Laradji, Abdellatif"],"dc:date":["2014-12-17T23:17:47Z","10000-01-01","1993"],"dc:description":["p-Radical p-blocks of finite group algebras are studied. Much of the p-radical group theory is generalized to p-blocks through R. Knorr's work on simple induction and restriction pairs. In addition, several results concerning such blocks are proved.","The most interesting fact known about p-radical groups is a result of T. Okuyama, who showed that such groups are p-solvable. It turns out that the same conclusion could be reached assuming much less. In fact, it is shown that finite groups, whose principal p-blocks are p-radical, are p-solvable. This is not in general true for non-principal blocks as illustrated by some examples. Nevertheless, in any case, simple modules in p-radical blocks behave somewhat like those in blocks of p-solvable groups.","A p-block, in which every (modular) simple module has vertices contained in the kernel, is characterized. Such a block enjoys a property much stronger than p-radicality. If, in addition, every simple module in this block has vertices conjugate to a defect group of the block, further characterizations are derived. As a consequence, some characterizations of p-length 1 p-solvable groups, in terms of the ordinary irreducible characters of the principal p-blocks, are given.","Made available in DSpace on 2014-12-17T23:17:47Z (GMT). No. of bitstreams: 1 9329091.pdf: 2515719 bytes, checksum: 59d3bc2a6181018bc344209affc81353 (MD5) Previous issue date: 1993","Embargo set by: Seth Robbins for item 72708 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","77 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1993."],"dc:identifier":["http://hdl.handle.net/2142/72540","(UMI)AAI9329091"],"dc:subject":["Mathematics"],"dc:title":["On P-Radical P-Blocks of Group Algebras"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:07Z"}