University of Illinois Urbana-Champaign

The Mod -3 Cohomology Ring of the O'Nan Sporadic Simple Group

McLallen, Nicola Whitley

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Description

Title
The Mod -3 Cohomology Ring of the O'Nan Sporadic Simple Group
Author(s)
McLallen, Nicola Whitley
Issue Date
2000
Doctoral Committee Chair(s)
Dade, Everett C.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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 ).
Graduation Semester
2000
Type of Resource
text
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