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https://hdl.handle.net/2142/86998
Description
Title
A Reduction for Dade's Conjecture
Author(s)
Schwartz, Gary Keith
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
Although the 'Inductive' form of Dade's conjecture must be verified for all finite, non-abelian, simple groups G, for most such G it suffices to verify a simpler form of the conjecture. In this thesis we will introduce two new forms of Dade's Conjecture, the Augmented Extended Projective Conjecture and the Augmented Inductive Conjecture, and prove that the Augmented Extended Projective Conjecture implies the Augmented Inductive Conjecture for all finite non-abelian simple groups except possibly for the Chevalley groups of types Aℓ, Dℓ, 2Aℓ, and 2Dℓ.
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