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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 UrbanaChampaign 
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 mod2 cohomology rings have been computed, but for p odd, less work has been done. In this thesis, the mod3 cohomology ring H* (ON, F3 ) of the O'Nan sporadic simple group ON is computed. Since the Sylow 3subgroups 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 nonmodular 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 UrbanaChampaign, 2000. 
URI:  http://hdl.handle.net/2142/86996 
Other Identifier(s):  (MiAaPQ)AAI9971133 
Date Available in IDEALS:  20150928 
Date Deposited:  2000 
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Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois