Character Theory for the Odd Order Theorem
The famous theorem of W. Feit and J. G. Thompson states that every group of odd order is solvable, and the proof of this has roughly two parts. The first appeared in Bender and Glauberman's Local Analysis for the Odd Order Theorem, number 188 in this series. The present book provides the character-theoretic second part and completes the proof. Thomas Peterfalvi also offers a revision of a theorem of Suzuki on split BN-pairs of rank one, a prerequisite for the classification of finite simple groups.
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abelian action acts acts fixed-point-freely additive algebraic Appendix applied Assume Hypothesis automorphism centralizes CF(G CG(X Chapter coherent conclusion conjugate contains contradiction cyclic defined Definition denote distinct divides element elementary abelian extension fact field finite group fixed points follows Frobenius group functions geometry given group with kernel holds Hypothesis 5.2 identified implies independent indices induced Indy integer involution Irr H Irr(G irreducible character isomorphic Kapitel Lemma Let G Let H linear mapping maximal subgroup Moreover nilpotent normal subgroup notation obtain odd order orthogonal particular prime prime divisor prime number Proof Proposition proves relative respectively satisfies structure subgroup of G subset Suppose Suzuki 2-group Sylow Theorem theory TI-subset of G transitive vanishes whence Z[Irr G