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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.","Made available in DSpace on 2015-09-28T15:20:33Z (GMT). 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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.","Made available in DSpace on 2015-09-28T15:20:33Z (GMT). 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