Products Of Finite Groups
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Author | : Adolfo Ballester-Bolinches |
Publisher | : Walter de Gruyter |
Total Pages | : 347 |
Release | : 2010-10-19 |
Genre | : Mathematics |
ISBN | : 311022061X |
The study of finite groups factorised as a product of two or more subgroups has become a subject of great interest during the last years with applications not only in group theory, but also in other areas like cryptography and coding theory. It has experienced a big impulse with the introduction of some permutability conditions. The aim of this book is to gather, order, and examine part of this material, including the latest advances made, give some new approach to some topics, and present some new subjects of research in the theory of finite factorised groups. Some of the topics covered by this book include groups whose subnormal subgroups are normal, permutable, or Sylow-permutable, products of nilpotent groups, and an exhaustive structural study of totally and mutually permutable products of finite groups and their relation with classes of groups. This monograph is mainly addressed to graduate students and senior researchers interested in the study of products and permutability of finite groups. A background in finite group theory and a basic knowledge of representation theory and classes of groups is recommended to follow it.
Author | : Adolfo Ballester-Bolinches |
Publisher | : Walter de Gruyter |
Total Pages | : 347 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 3110204177 |
The study of finite groups factorised as a product of two or more subgroups has become a subject of great interest during the last years with applications not only in group theory, but also in other areas like cryptography and coding theory. It has experienced a big impulse with the introduction of some permutability conditions. The aim of this book is to gather, order, and examine part of this material, including the latest advances made, give some new approach to some topics, and present some new subjects of research in the theory of finite factorised groups. Some of the topics covered by this book include groups whose subnormal subgroups are normal, permutable, or Sylow-permutable, products of nilpotent groups, and an exhaustive structural study of totally and mutually permutable products of finite groups and their relation with classes of groups. This monograph is mainly addressed to graduate students and senior researchers interested in the study of products and permutability of finite groups. A background in finite group theory and a basic knowledge of representation theory and classes of groups is recommended to follow it.
Author | : Tullio Ceccherini-Silberstein |
Publisher | : Cambridge University Press |
Total Pages | : 177 |
Release | : 2014-01-16 |
Genre | : Mathematics |
ISBN | : 1107627850 |
A self-contained introduction to the representation theory and harmonic analysis of wreath products of finite groups, with examples and exercises.
Author | : H.E. Rose |
Publisher | : Springer Science & Business Media |
Total Pages | : 314 |
Release | : 2009-12-16 |
Genre | : Mathematics |
ISBN | : 1848828896 |
Introduces the richness of group theory to advanced undergraduate and graduate students, concentrating on the finite aspects. Provides a wealth of exercises and problems to support self-study. Additional online resources on more challenging and more specialised topics can be used as extension material for courses, or for further independent study.
Author | : I. Martin Isaacs |
Publisher | : American Mathematical Society |
Total Pages | : 368 |
Release | : 2023-01-24 |
Genre | : Mathematics |
ISBN | : 1470471604 |
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.
Author | : Tullio Ceccherini-Silberstein |
Publisher | : Springer Science & Business Media |
Total Pages | : 446 |
Release | : 2010-08-24 |
Genre | : Computers |
ISBN | : 3642140343 |
Cellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory, symbolic dynamics, and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups, and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. The volume is entirely self-contained, with 10 appendices and more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. It provides a comprehensive account of recent progress in the theory of cellular automata based on the interplay between amenability, geometric and combinatorial group theory, symbolic dynamics and the algebraic theory of group rings which are treated here for the first time in book form.
Author | : Jean Pierre Serre |
Publisher | : |
Total Pages | : 170 |
Release | : 1996 |
Genre | : |
ISBN | : |
Author | : Daniel Gorenstein |
Publisher | : Springer Science & Business Media |
Total Pages | : 339 |
Release | : 2013-11-27 |
Genre | : Mathematics |
ISBN | : 1468484974 |
In February 1981, the classification of the finite simple groups (Dl)* was completed,t. * representing one of the most remarkable achievements in the history or mathematics. Involving the combined efforts of several hundred mathematicians from around the world over a period of 30 years, the full proof covered something between 5,000 and 10,000 journal pages, spread over 300 to 500 individual papers. The single result that, more than any other, opened up the field and foreshadowed the vastness of the full classification proof was the celebrated theorem of Walter Feit and John Thompson in 1962, which stated that every finite group of odd order (D2) is solvable (D3)-a statement expressi ble in a single line, yet its proof required a full 255-page issue of the Pacific 10urnal of Mathematics [93]. Soon thereafter, in 1965, came the first new sporadic simple group in over 100 years, the Zvonimir Janko group 1 , to further stimulate the 1 'To make the book as self-contained as possible. we are including definitions of various terms as they occur in the text. However. in order not to disrupt the continuity of the discussion. we have placed them at the end of the Introduction. We denote these definitions by (DI). (D2), (D3). etc.
Author | : Volodymyr Nekrashevych |
Publisher | : American Mathematical Soc. |
Total Pages | : 248 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821838318 |
Self-similar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc. This book studies the self-similarity phenomenon in group theory and shows its intimate relationship with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. This connection is established through the central topics of the book, which are the notions of the iterated monodromy group and limit space. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. In particular, it is shown that Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties can appear not just as isolated examples, but as naturally defined iterated monodromy groups of rational functions. The book offers important, new mathematics that will open new avenues of research in group theory and dynamical systems. It is intended to be accessible to a wide readership of professional mathematicians.
Author | : Benjamin Steinberg |
Publisher | : Springer Science & Business Media |
Total Pages | : 166 |
Release | : 2011-10-23 |
Genre | : Mathematics |
ISBN | : 1461407761 |
This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.