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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acts regularly acts without fixed additive group algebraic Appendix Assume Hypothesis 11.2 automorphism central extension CF(G CG(P CG(x Chapter character of G character theory coherent conjugacy classes conjugate contradiction Cq(P Cq(X Cs(P cyclic Dade isometry relative denote divides doubly transitive element elementary abelian F x F Feit-Thompson Theorem finite group fixed points follows Frobenius group G of Type group of odd group with kernel Hall subgroup holds Hypothesis 5.2 induced Indw integer involution Irr(G irreducible character irreducible component isomorphic Kapitel Lemma Let G Let H maximal subgroup mod q near-field NG(P nilpotent normal subgroup notation odd order order prime orthogonal prime divisor prime number Proof Proposition quadratic mapping S/Qo satisfies Satz st has order subgroup of G subgroups of Type Suppose Suzuki 2-group Sylow p-subgroup Theorem 8.8 Tl-subset of G vanishes vector space virtual character whence Z[IrrG