Finite Group Theory (Graduate Studies in Mathematics, Vol. 92) (Graduate Studies in Mathematics, 92)

The text begins with a review of group actions and Sylow theory. It includes semidirect products, the Schur-Zassenhaus theorem, the theory of commutators, coprime actions on groups, transfer theory, Frobenius groups, primitive and multiply transitive permutation groups, the simplicity of the PSL groups, the generalized Fitting subgroup and also Thompson's J-subgroup and his normal $p$-complement theorem. Topics that seldom (or never) appear in books are also covered. These include subnormality theory, a group-theoretic proof of Burnside's theorem about groups with order divisible by just two primes, the Wielandt automorphism tower theorem, Yoshida's transfer theorem, the ``principal ideal theorem'' of transfer theory and many smaller results that are not very well known. Proofs often contain original ideas, and they are given in complete detail. In many cases they are simpler than can be found elsewhere. The book is largely based on the author's lectures, and consequently, the style is friendly and somewhat informal. Finally, the book includes a large collection of problems at disparate levels of difficulty. These should enable students to practice group theory and not just read about it. Martin Isaacs is professor of mathematics at the University of Wisconsin, Madison. Over the years, he has received many teaching awards and is well known for his inspiring teaching and lecturing. He received the University of Wisconsin Distinguished Teaching Award in 1985, the Benjamin Smith Reynolds Teaching Award in 1989, and the Wisconsin Section MAA Teaching Award in 1993, to name only a few. He was also honored by being the selected MAA Polya Lecturer in 2003-2005.

the Text Begins With A Review Of Group Actions And Sylow Theory. It Includes Semidirect Products, The Schur-zassenhaus Theorem, The Theory Of Commutators, Coprime Actions On Groups, Transfer Theory, Frobenius Groups, Primitive And Multiply Transitive Permutation Groups, The Simplicity Of The Psl Groups, The Generalized Fitting Subgroup And Also Thompson's J-subgroup And His Normal $p$-complement Theorem. Topics That Seldom (or Never) Appear In Books Are Also Covered. These Include Subnormality Theory, A Group-theoretic Proof Of Burnside's Theorem About Groups With Order Divisible By Just Two Primes, The Wielandt Automorphism Tower Theorem, Yoshida's Transfer Theorem, The ``principal Ideal Theorem'' Of Transfer Theory And Many Smaller Results That Are Not Very Well Known. Proofs Often Contain Original Ideas, And They Are Given In Complete Detail. In Many Cases They Are Simpler Than Can Be Found Elsewhere. The Book Is Largely Based On The Author's Lectures, And Consequently, The Style Is Friendly And Somewhat Informal. Finally, The Book Includes A Large Collection Of Problems At Disparate Levels Of Difficulty. These Should Enable Students To Practice Group Theory And Not Just Read About It. Martin Isaacs Is Professor Of Mathematics At The University Of Wisconsin, Madison. Over The Years, He Has Received Many Teaching Awards And Is Well-known For His Inspiring Teaching And Lecturing. He Received The University Of Wisconsin Distinguished Teaching Award In 1985, The Benjamin Smith Reynolds Teaching Award In 1989, And The Wisconsin Section Maa Teaching Award In 1993 To Name Only A Few. He Was Also Honored By Being The Selected Maa Polya Lecturer In 2003-2005.

The text begins with a review of group actions and Sylow theory. It includes semidirect products, the Schur–Zassenhaus theorem, the theory of commutators, coprime actions on groups, transfer theory, Frobenius groups, primitive and multiply transitive permutation groups, the simplicity of the PSL groups, the generalized Fitting subgroup and also Thompson's J-subgroup and his normal $p$-complement theorem. Topics that seldom (or never) appear in books are also covered. These include subnormality theory, a group-theoretic proof of Burnside's theorem about groups with order divisible by just two primes, the Wielandt automorphism tower theorem, Yoshida's transfer theorem, the “principal ideal theorem” of transfer theory and many smaller results that are not very well known. Proofs often contain original ideas, and they are given in complete detail. In many cases they are simpler than can be found elsewhere. The book is largely based on the author's lectures, and consequently, the style is friendly and somewhat informal. Finally, the book includes a large collection of problems at disparate levels of difficulty. These should enable students to practice group theory and not just read about it. Martin Isaacs is professor of mathematics at the University of Wisconsin, Madison. Over the years, he has received many teaching awards and is well known for his inspiring teaching and lecturing. He received the University of Wisconsin Distinguished Teaching Award in 1985, the Benjamin Smith Reynolds Teaching Award in 1989, and the Wisconsin Section MAA Teaching Award in 1993, to name only a few. He was also honored by being the selected MAA Pólya Lecturer in 2003–2005. This book is a companion volume to Graduate Algebra: Commutative View (published as volume 73 in this series). The main and most important feature of the book is that it presents a unified approach to many important topics, such as group theory, ring theory, Lie algebras, and gives conceptual proofs of many basic results of noncommutative algebra. There are also a number of major results in noncommutative algebra that are usually found only in technical works, such as Zelmanov's proof of the restricted Burnside problem in group theory, word problems in groups, Tits's alternative in algebraic groups, PI algebras, and many of the roles that Coxeter diagrams play in algebra. The first half of the book can serve as a one-semester course on noncommutative algebra, whereas the remaining part of the book describes some of the major directions of research in the past 100 years. The main text is extended through several appendices, which permits the inclusion of more advanced material, and numerous exercises. The only prerequisite for using the book is an undergraduate course in algebra; whenever necessary, results are quoted from Graduate Algebra: Commutative View. This Book Is An Expanded Text For A Graduate Course In Commutative Algebra, Focusing On The Algebraic Underpinnings Of Algebraic Geometry And Of Number Theory. Accordingly, The Theory Of Affine Algebras Is Featured, Treated Both Directly And Via The Theory Of Noetherian And Artinian Modules, And The Theory Of Graded Algebras Is Included To Provide The Foundation For Projective Varieties.--jacket. Louis Halle Rowen. Includes Bibliographical References (p. 627-634) And Index. Sylow theory Subnormality Split extensions Commutators Transfer Frobenius actions The Thompson subgroup Permutation groups More on subnormality More transfer theory.