2026-09-22T01:51:37Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/86996 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

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 Dade, Everett C. McLallen, Nicola Whitley 2015-09-28T15:20:32Z 2015-09-28T15:20:32Z 10000-01-01 2000 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. http://hdl.handle.net/2142/86996 (MiAaPQ)AAI9971133 eng Mathematics The Mod -3 Cohomology Ring of the O'Nan Sporadic Simple Group text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.