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 Title: The Mod -3 Cohomology Ring of the O'Nan Sporadic Simple Group Author(s): McLallen, Nicola Whitley Doctoral Committee Chair(s): Dade, Everett C. Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: 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 ). Issue Date: 2000 Type: Text Language: English Description: 90 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000. URI: http://hdl.handle.net/2142/86996 Other Identifier(s): (MiAaPQ)AAI9971133 Date Available in IDEALS: 2015-09-28 Date Deposited: 2000
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