{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86996"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86996","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The Mod -3 Cohomology Ring of the O'Nan Sporadic Simple Group","abstract":"Made available in DSpace on 2015-09-28T15:20:32Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9971133.pdf: 2632403 bytes, checksum: eb61ec5e102acf5fb7e5bd746d5c8b41 (MD5) Previous issue date: 2000","abstract_html":"Made available in DSpace on 2015-09-28T15:20:32Z (GMT). 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No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9971133.pdf: 2632403 bytes, checksum: eb61ec5e102acf5fb7e5bd746d5c8b41 (MD5) Previous issue date: 2000","In recent years, there has been interest in computing the mod- p (for p a prime) cohomology rings of finite groups and, in particular, the finite simple groups. Many of the mod-2 cohomology rings have been computed, but for p odd, less work has been done. In this thesis, the mod-3 cohomology ring H* (ON, F3 ) of the O'Nan sporadic simple group ON is computed. Since the Sylow 3-subgroups of ON are abelian, classical group cohomology results imply that the cohomology ring H* (ON, F3 ) can be computed as the algebra of invariants of the action of a certain group G on a polynomial algebra tensored with an exterior algebra over F3 . The order of G is not divisible by 3, so classical non-modular methods of invariant theory, including Molien's Theorem and the Reynolds Operator, could be used to compute the invariant algebra. With the aid of the computer algebra software MAGMA and Macaulay 2, these methods are used to compute a complete list of generators for H* (ON, F3 ).","Embargo set by: Seth Robbins for item 88277 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","90 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000."]},{"key":"dc:title","label":"Title","values":["The Mod -3 Cohomology Ring of the O'Nan Sporadic Simple Group"]}]}],"canonical_facts":{"dc:contributor":["Dade, Everett C."],"dc:creator":["McLallen, Nicola Whitley"],"dc:date":["2015-09-28T15:20:32Z","10000-01-01","2000"],"dc:description":["Made available in DSpace on 2015-09-28T15:20:32Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9971133.pdf: 2632403 bytes, checksum: eb61ec5e102acf5fb7e5bd746d5c8b41 (MD5) Previous issue date: 2000","In recent years, there has been interest in computing the mod- p (for p a prime) cohomology rings of finite groups and, in particular, the finite simple groups. Many of the mod-2 cohomology rings have been computed, but for p odd, less work has been done. In this thesis, the mod-3 cohomology ring H* (ON, F3 ) of the O'Nan sporadic simple group ON is computed. Since the Sylow 3-subgroups of ON are abelian, classical group cohomology results imply that the cohomology ring H* (ON, F3 ) can be computed as the algebra of invariants of the action of a certain group G on a polynomial algebra tensored with an exterior algebra over F3 . The order of G is not divisible by 3, so classical non-modular methods of invariant theory, including Molien's Theorem and the Reynolds Operator, could be used to compute the invariant algebra. With the aid of the computer algebra software MAGMA and Macaulay 2, these methods are used to compute a complete list of generators for H* (ON, F3 ).","Embargo set by: Seth Robbins for item 88277 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","90 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000."],"dc:identifier":["http://hdl.handle.net/2142/86996","(MiAaPQ)AAI9971133"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["The Mod -3 Cohomology Ring of the O'Nan Sporadic Simple Group"],"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":"2026-07-22T22:26:28Z"}