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512.54 --- 512.54 Groups. Group theory --- Groups. Group theory --- Infinite groups --- Solvable groups --- Soluble groups --- Group theory --- Groups, Infinite

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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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Finite groups. --- Solvable groups. --- Group theory --- Groupes, Théorie des --- Solvable groups --- Groupes résolubles --- Soluble groups --- Groups, Finite --- Modules (Algebra) --- Groupes, Théorie des. --- Groupes résolubles. --- Groupes finis --- Groupes résolubles. --- Groupes, Théorie des.

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Lectures on Finitely Generated Solvable Groups are based on the “Topics in Group Theory" course focused on finitely generated solvable groups that was given by Gilbert G. Baumslag at the Graduate School and University Center of the City University of New York.  While knowledge about finitely generated nilpotent groups is extensive, much less is known about the more general class of solvable groups containing them.  The study of finitely generated solvable groups involves many different threads; therefore these notes contain discussions on HNN extensions; amalgamated and wreath products; and other concepts from combinatorial group theory as well as commutative algebra.  Along with Baumslag’s Embedding Theorem for Finitely Generated Metabelian Groups, two theorems of Bieri and Strebel are presented to provide a solid foundation for understanding the fascinating class of finitely generated solvable groups.  Examples are also supplied, which help illuminate many of the key concepts contained in the notes.  Requiring only a modest initial group theory background from graduate and post-graduate students, these notes provide a field guide to the class of finitely generated solvable groups from a combinatorial group theory perspective.

Functions of several complex variables. --- Mathematics. --- Solvable groups. --- Combinatorial analysis --- Mathematics --- Algebra --- Group theory --- Physical Sciences & Mathematics --- Combinatorial group theory. --- Soluble groups --- Combinatorial groups --- Groups, Combinatorial --- Algebra. --- Commutative algebra. --- Commutative rings. --- Group theory. --- Combinatorics. --- Group Theory and Generalizations. --- General Algebraic Systems. --- Commutative Rings and Algebras. --- Mathematical analysis --- Combinatorics --- Groups, Theory of --- Substitutions (Mathematics) --- Rings (Algebra)