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 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 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 Infinite Abelian Groups written by Irving Kaplansky and published by Courier Dover Publications. This book was released on 2018-12-18 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the Introduction to this concise monograph, the author states his two main goals: first, "to make the theory of infinite abelian groups available in a convenient form to the mathematical public; second, to help students acquire some of the techniques used in modern infinite algebra." Suitable for advanced undergraduates and graduate students in mathematics, the text requires no extensive background beyond the rudiments of group theory. Starting with examples of abelian groups, the treatment explores torsion groups, Zorn's lemma, divisible groups, pure subgroups, groups of bounded order, and direct sums of cyclic groups. Subsequent chapters examine Ulm's theorem, modules and linear transformations, Banach spaces, valuation rings, torsion-free and complete modules, algebraic compactness, characteristic submodules, and the ring of endomorphisms. Many exercises appear throughout the book, along with a guide to the literature and a detailed bibliography.
Download or read book The Classification of Minimal Graphs with Given Abelian Automorphism Group written by William C. Arlinghaus and published by American Mathematical Soc.. This book was released on 1985 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Any finite abstract group can be realized as the automorphism group of a graph. The purpose of this memoir is to find the realization, for each finite abelian group, with the least number of vertices possible. The results are extended to all finite abelian groups. Thus a complete classification is provided for minimal graphs with given finite abelian automorphism group.
Download or read book The Automorphism Group of a Finite Abelian Primary Group written by Susan Thorbrogger Monroe and published by . This book was released on 1970 with total page 58 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 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 Automorphisms of Finite Groups written by Inder Bir S. Passi and published by . This book was released on 2018 with total page 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 Cellular Automata and Groups written by Tullio Ceccherini-Silberstein and published by Springer Science & Business Media. This book was released on 2010-08-24 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fourier Analysis on Finite Abelian Groups written by Bao Luong and published by Springer Science & Business Media. This book was released on 2009-08-14 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. This text introduces mathematics students to subjects that are within their reach, but it also has powerful applications that may appeal to advanced researchers and mathematicians. The only prerequisites necessary are group theory, linear algebra, and complex analysis.
Download or read book The Automorphism Groups of Abelian P groups written by Kurt Augustus Hirsch and published by . This book was released on 1961 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Torsion free Abelian Groups Whose Automorphism Groups are Finite written by J. T. Hallett and published by . This book was released on 1961 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Abelian Groups written by László Fuchs and published by Springer. This book was released on 2015-12-12 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the subject’s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of un decidability problems. The treatment of the latter trend includes Shelah’s seminal work on the un decidability in ZFC of Whitehead’s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology and homological algebra. An abundance of exercises are included to test the reader’s comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject’s further development.
Download or read book Abelian Groups Rings and Modules written by Andrei V. Kelarev and published by American Mathematical Soc.. This book was released on 2001 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings from the conference on Abelian Groups, Rings, and Modules (AGRAM) held at the University of Western Australia (Perth). Included are articles based on talks given at the conference, as well as a few specially invited papers. The proceedings were dedicated to Professor László Fuchs. The book includes a tribute and a review of his work by his long-time collaborator, Professor Luigi Salce. Four surveys from leading experts follow Professor Salce's article. They present recent results from active research areas
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 Infinite Abelian Groups written by László Fuchs and published by . This book was released on 1970 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
