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In 1963 Walter Feit and John G. Thompson published a proof of a 1911 conjecture by Burnside that every finite group of odd order is solvable. This proof, which ran for 255 pages, was a tour-de-force of mathematics and inspired intense effort to classify finite simple groups. This book presents a revision and expansion of the first half of the proof of the Feit-Thompson theorem. Simpler, more detailed proofs are provided for some intermediate theorems. Recent results are used to shorten other proofs. The book will make the first half of this remarkable proof accessible to readers familiar with just the rudiments of group theory.

Feit-Thompson theorem. --- Solvable groups. --- Soluble groups --- Group theory --- Odd order theorem --- Order theorem, Odd --- Theorem, Feit-Thompson --- Theorem, Odd order --- Finite groups --- Solvable groups

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The famous and important 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 part appeared in Bender and Glauberman's Local Analysis for the Odd Order Theorem which was number 188 in this series. This book, first published in 2000, provides the character-theoretic second part and thus completes the proof. Also included here is a revision of a theorem of Suzuki on split BN-pairs of rank one; a prerequisite for the classification of finite simple groups. All researchers in group theory should have a copy of this book in their library.

Feit-Thompson theorem. --- Finite groups. --- Characters of groups. --- Odd order theorem --- Order theorem, Odd --- Theorem, Feit-Thompson --- Theorem, Odd order --- Finite groups --- Solvable groups --- Characters, Group --- Group characters --- Groups, Characters of --- Representations of groups --- Rings (Algebra) --- Groups, Finite --- Group theory --- Modules (Algebra)