Download or read book Counting the Number of Automorphisms of Finite Abelian Groups written by Linda J. Krause and published by . This book was released on 1994 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automorphisms of Finite Groups written by Inder Bir Singh Passi and published by Springer. This book was released on 2019-01-12 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts: the first part offers an exposition of the fundamental exact sequence of Wells that relates automorphisms, derivations and cohomology of groups, along with some interesting applications of the sequence. The second part offers an account of important developments on a conjecture that a finite group has at least a prescribed number of automorphisms if the order of the group is sufficiently large. A non-abelian group of prime-power order is said to have divisibility property if its order divides that of its automorphism group. The final part of the book discusses the literature on divisibility property of groups culminating in the existence of groups without this property. Unifying various ideas developed over the years, this largely self-contained book includes results that are either proved or with complete references provided. It is aimed at researchers working in group theory, in particular, graduate students in algebra.
Download or read book Some Subgroups of the Automorphism Group of a Finite Abelian Group written by William Lee Hightower and published by . This book was released on 1970 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Study of the Automorphisms of Finite Abelian Groups with Emphasis on Cyclic Groups written by Glenn Alan Hawkins and published by . This book was released on 1962 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Abelian Groups written by L. Fuchs and published by Elsevier. This book was released on 2014-07-15 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abelian Groups deals with the theory of abelian or commutative groups, with special emphasis on results concerning structure problems. More than 500 exercises of varying degrees of difficulty, with and without hints, are included. Some of the exercises illuminate the theorems cited in the text by providing alternative developments, proofs or counterexamples of generalizations. Comprised of 16 chapters, this volume begins with an overview of the basic facts on group theory such as factor group or homomorphism. The discussion then turns to direct sums of cyclic groups, divisible groups, and direct summands and pure subgroups, as well as Kulikov's basic subgroups. Subsequent chapters focus on the structure theory of the three main classes of abelian groups: the primary groups, the torsion-free groups, and the mixed groups. Applications of the theory are also considered, along with other topics such as homomorphism groups and endomorphism rings; the Schreier extension theory with a discussion of the group of extensions and the structure of the tensor product. In addition, the book examines the theory of the additive group of rings and the multiplicative group of fields, along with Baer's theory of the lattice of subgroups. This book is intended for young research workers and students who intend to familiarize themselves with abelian groups.
Download or read book Intense Automorphisms of Finite Groups written by Mima Stanojkovski and published by American Mathematical Society. This book was released on 2021-12-09 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Finitely Generated Abelian Groups and Similarity of Matrices over a Field written by Christopher Norman and published by Springer Science & Business Media. This book was released on 2012-01-25 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part 1 of this book provides a measured introduction to such groups: two finitely generated abelian groups are isomorphic if and only if their invariant factor sequences are identical. The analogous theory of matrix similarity over a field is then developed in Part 2 starting with matrices having polynomial entries: two matrices over a field are similar if and only if their rational canonical forms are equal. Under certain conditions each matrix is similar to a diagonal or nearly diagonal matrix, namely its Jordan form. The reader is assumed to be familiar with the elementary properties of rings and fields. Also a knowledge of abstract linear algebra including vector spaces, linear mappings, matrices, bases and dimension is essential, although much of the theory is covered in the text but from a more general standpoint: the role of vector spaces is widened to modules over commutative rings. Based on a lecture course taught by the author for nearly thirty years, the book emphasises algorithmic techniques and features numerous worked examples and exercises with solutions. The early chapters form an ideal second course in algebra for second and third year undergraduates. The later chapters, which cover closely related topics, e.g. field extensions, endomorphism rings, automorphism groups, and variants of the canonical forms, will appeal to more advanced students. The book is a bridge between linear and abstract algebra.
Download or read book Notes on Counting An Introduction to Enumerative Combinatorics written by Peter J. Cameron and published by Cambridge University Press. This book was released on 2017-06-29 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to enumerative combinatorics, vital to many areas of mathematics. It is suitable as a class text or for individual study.
Download or read book Infinite Abelian Groups written by Irving Kaplansky and published by . This book was released on 1969 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Actions of Finite Abelian Groups written by Czes Kosniowski and published by Pitman Publishing. This book was released on 1978 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Directions in Number Theory written by Ellen E. Eischen and published by Springer. This book was released on 2016-09-26 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring the interplay between deep theory and intricate computation, this volume is a compilation of research and survey papers in number theory, written by members of the Women In Numbers (WIN) network, principally by the collaborative research groups formed at Women In Numbers 3, a conference at the Banff International Research Station in Banff, Alberta, on April 21-25, 2014. The papers span a wide range of research areas: arithmetic geometry; analytic number theory; algebraic number theory; and applications to coding and cryptography. The WIN conference series began in 2008, with the aim of strengthening the research careers of female number theorists. The series introduced a novel research-mentorship model: women at all career stages, from graduate students to senior members of the community, joined forces to work in focused research groups on cutting-edge projects designed and led by experienced researchers. The goals for Women In Numbers 3 were to establish ambitious new collaborations between women in number theory, to train junior participants about topics of current importance, and to continue to build a vibrant community of women in number theory. Forty-two women attended the WIN3 workshop, including 15 senior and mid-level faculty, 15 junior faculty and postdocs, and 12 graduate students.
Download or read book The Automorphism Groups of Finite Abelian Groups written by 李盈嬌 and published by . This book was released on 2003 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamical Systems of Algebraic Origin written by Klaus Schmidt and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing a class of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which nevertheless lends itself to systematic study: the Zd-actions by automorphisms of compact, abelian groups. One aspect of these actions, not surprising in itself but quite striking in its extent and depth nonetheless, is the connection with commutative algebra and arithmetical algebraic geometry. The algebraic framework resulting from this connection allows the construction of examples with a variety of specified dynamical properties, and by combining algebraic and dynamical tools one obtains a quite detailed understanding of this class of Zd-actions.
Download or read book Algorithmic Bioprocesses written by Anne Condon and published by Springer Science & Business Media. This book was released on 2009-08-14 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fundamental understanding of algorithmic bioprocesses is key to learning how information processing occurs in nature at the cell level. The field is concerned with the interactions between computer science on the one hand and biology, chemistry, and DNA-oriented nanoscience on the other. In particular, this book offers a comprehensive overview of research into algorithmic self-assembly, RNA folding, the algorithmic foundations for biochemical reactions, and the algorithmic nature of developmental processes. The editors of the book invited 36 chapters, written by the leading researchers in this area, and their contributions include detailed tutorials on the main topics, surveys of the state of the art in research, experimental results, and discussions of specific research goals. The main subjects addressed are sequence discovery, generation, and analysis; nanoconstructions and self-assembly; membrane computing; formal models and analysis; process calculi and automata; biochemical reactions; and other topics from natural computing, including molecular evolution, regulation of gene expression, light-based computing, cellular automata, realistic modelling of biological systems, and evolutionary computing. This subject is inherently interdisciplinary, and this book will be of value to researchers in computer science and biology who study the impact of the exciting mutual interaction between our understanding of bioprocesses and our understanding of computation.
Download or read book Infinite Abelian Groups written by and published by Academic Press. This book was released on 1970-01-01 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite Abelian Groups
Download or read book Dynamics Topology and Numbers written by Pieter Moree and published by American Mathematical Soc.. This book was released on 2020-02-12 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
Download or read book P Automorphisms of Finite P Groups written by Evgenii I. Khukhro and published by Cambridge University Press. This book was released on 1998-02-13 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers working in group theory and Lie rings.
