Fundamentals Of Group Theory
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Fundamentals of Group Theory
Author: Steven Roman
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-10-26
Fundamentals of Group Theory provides a comprehensive account of the basic theory of groups. Both classic and unique topics in the field are covered, such as an historical look at how Galois viewed groups, a discussion of commutator and Sylow subgroups, and a presentation of Birkhoff’s theorem. Written in a clear and accessible style, the work presents a solid introduction for students wishing to learn more about this widely applicable subject area. This book will be suitable for graduate courses in group theory and abstract algebra, and will also have appeal to advanced undergraduates. In addition it will serve as a valuable resource for those pursuing independent study. Group Theory is a timely and fundamental addition to literature in the study of groups.
Fundamentals of the Theory of Groups
Author: Mikhail Ivanovich Kargapolov
language: en
Publisher: Springer
Release Date: 1979-12-06
The present edition differs from the first in several places. In particular our treatment of polycyclic and locally polycyclic groups-the most natural generalizations of the classical concept of a finite soluble group-has been expanded. We thank Ju. M. Gorcakov, V. A. Curkin and V. P. Sunkov for many useful remarks. The Authors Novosibirsk, Akademgorodok, January 14, 1976. v Preface to the First Edition This book consists of notes from lectures given by the authors at Novosi birsk University from 1968 to 1970. Our intention was to set forth just the fundamentals of group theory, avoiding excessive detail and skirting the quagmire of generalizations (however a few generalizations are nonetheless considered-see the last sections of Chapters 6 and 7). We hope that the student desiring to work in the theory of groups, having become acquainted with its fundamentals from these notes, will quickly be able to proceed to the specialist literature on his chosen topic. We have striven not to cross the boundary between abstract and scholastic group theory, elucidating difficult concepts by means of simple examples wherever possible. Four types of examples accompany the theory: numbers under addition, numbers under multiplication, permutations, and matrices.
Basics of Representation Theory
Author: Udayan Bhattacharya
language: en
Publisher: Educohack Press
Release Date: 2025-02-20
Delve into the captivating world of "Basics of Representation Theory," a comprehensive guide designed for students, researchers, and enthusiasts eager to explore the intricate symmetries and structures that underpin modern mathematics. Our book offers a detailed introduction to foundational concepts, providing a solid understanding of group actions, linear representations, and character theory. From there, it explores the algebraic structures of irreducible representations, breaking down the decomposition into irreducible components and examining the properties of characters. Readers will journey through diverse topics, including the representation theory of symmetric groups, Lie groups, and algebraic groups, as well as advanced topics such as the representation theory of finite groups, the Langlands program, and applications in quantum mechanics and number theory. With a wealth of examples, illustrations, and exercises, "Basics of Representation Theory" ensures a hands-on approach to learning, encouraging practical exploration and problem-solving. The book also includes numerous references and further reading suggestions for those who wish to delve deeper into specific topics. Written in a clear and accessible style, this book caters to all levels, from undergraduate students encountering representation theory for the first time to experienced researchers seeking fresh insights. With its comprehensive coverage and diverse applications, "Basics of Representation Theory" is an invaluable resource for anyone interested in the beauty and depth of this field.