Download or read book Finite Groups of Outer Automorphisms of Free Groups of Finite Rank written by Yuxing Wang and published by . This book was released on 1996 with total page 180 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 Surface realizable Finite Groups of Outer Automorphisms of Finitely generated Free Groups written by Christopher Thomas and published by . This book was released on 2001 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: A homeomorphism from a punctured surface to itself induces an outer automorphism of the free fundamental group of the surface, an outer automorphism which can be called surface-realizable. This paper provides necessary and sufficient conditions for a finite abelian group of outer automorphisms of a finitely-generated free group to be surface-realizable. Furthermore, n.a.s.c. are given for any finite group of such outer automorphisms to be realized by orientation-preserving homeomorphisms of an orientable surface. These properties are identified by examining those finite subgroups of automorphisms which are mapped into the group of outer automorphisms by the usual projection, and making sure that the non-trivial automorphisms fix either a trivial or cyclic subgroup of the free group. Examples are given to show the difficulties in applying this method to non-abelian cases.
Download or read book The Maximum Order Finite Groups of Outer Automorphisms of Free Groups written by Sicheng Wang and published by . This book was released on 1993 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finiteness Conditions and Generalized Soluble Groups written by Derek J.S. Robinson and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a study of group theoretical properties of two disparate kinds, firstly finiteness conditions or generalizations of finiteness and secondly generalizations of solubility or nilpotence. It will be particularly interesting to discuss groups which possess properties of both types. The origins of the subject may be traced back to the nineteen twenties and thirties and are associated with the names of R. Baer, S.N. Cernikov, K.A. Hirsch, A.G. Kuros, 0.]. Schmidt and H. Wielandt. Since this early period, the body of theory has expanded at an increasingly rapid rate through the efforts of many group theorists, particularly in Germany, Great Britain and the Soviet Union. Some of the highest points attained can, perhaps, be found in the work of P. Hall and A.I. Mal'cev on infinite soluble groups. Kuras's well-known book "The theory of groups" has exercised a strong influence on the development of the theory of infinite groups: this is particularly true of the second edition in its English translation of 1955. To cope with the enormous increase in knowledge since that date, a third volume, containing a survey of the contents of a very large number of papers but without proofs, was added to the book in 1967
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 Centralizers of Finite Subgroups of Automorphisms and Outer Automorphisms of Free Groups written by Debra Lynn Boutin and published by . This book was released on 1998 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symmetric Automorphisms of Free Products written by Darryl McCullough and published by American Mathematical Soc.. This book was released on 1996 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors construct a complex [italic capital]K([italic capital]G) on which the automorphism group of [italic capital]G acts and use it to derive finiteness consequences for the group [capital Greek]Sigma [italic]Aut([italic capital]G). They prove that each component of [italic capital]K([italic capital]G) is contractible and describe the vertex stabilizers as elementary constructs involving the groups [italic capital]G[subscript italic]i and [italic]Aut([italic capital]G[subscript italic]i).
Download or read book Some Solvable Subgroups of the Outer Automorphism Group of a Finite Group written by Nguyen Cao Dam and published by . This book was released on 1972 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automorphisms of Free Groups of Finite Rank in the Variety AmA written by Athanassios I. Papistas and published by . This book was released on 1993 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite and Locally Finite Groups written by B. Hartley and published by Springer. This book was released on 1995-08-31 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Istanbul, Turkey, 14--27 August 1994
Download or read book Topics in Geometric Group Theory written by Pierre de la Harpe and published by University of Chicago Press. This book was released on 2000-10-15 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.
Download or read book Extended Abstracts Fall 2012 written by Juan González-Meneses and published by Springer. This book was released on 2014-07-24 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features seventeen extended conference abstracts corresponding to selected talks given by participants at the CRM research program “Automorphisms of Free Groups: Algorithms, Geometry and Dynamics”, which took place at the Centre de Recerca Matemàtica in Barcelona in fall 2012. Most of them are short articles giving preliminary presentations of new results not yet published in regular research journals. The articles are the result from a direct collaboration among active researchers in the area after working in a dynamic and productive atmosphere. The book is intended for established researchers in the area of Group Theory, as well as for PhD and postdoc students who wish to learn more about the latest advances in this active area of research.
Download or read book The Classification of the Finite Simple Groups Number 7 written by Daniel Gorenstein and published by American Mathematical Soc.. This book was released on 2018-02-15 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classification of finite simple groups is a landmark result of modern mathematics. The multipart series of monographs which is being published by the AMS (Volume 40.1–40.7 and future volumes) represents the culmination of a century-long project involving the efforts of scores of mathematicians published in hundreds of journal articles, books, and doctoral theses, totaling an estimated 15,000 pages. This part 7 of the series is the middle of a trilogy (Volume 40.5, Volume 40.7, and forthcoming Volume 40.8) treating the Generic Case, i.e., the identification of the alternating groups of degree at least 13 and most of the finite simple groups of Lie type and Lie rank at least 4. Moreover, Volumes 40.4–40.8 of this series will provide a complete treatment of the simple groups of odd type, i.e., the alternating groups (with two exceptions) and the groups of Lie type defined over a finite field of odd order, as well as some of the sporadic simple groups. In particular, this volume completes the construction, begun in Volume 40.5, of a collection of neighboring centralizers of a particularly nice form. All of this is then applied to complete the identification of the alternating groups of degree at least 13. The book is suitable for graduate students and researchers interested in the theory of finite groups.
Download or read book Groups Languages and Geometry written by Robert H. Gilman and published by American Mathematical Soc.. This book was released on 1999 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Geometric Group Theory and Computer Science held at Mount Holyoke College (South Hadley, MA). The conference was devoted to computational aspects of geometric group theory, a relatively young area of research which has grown out of an influx of ideas from topology and computer science into combinatorial group theory. The book reflects recent progress in this interesting new field. Included are articles about insights from computer experiments, applications of formal language theory, decision problems, and complexity problems. There is also a survey of open questions in combinatorial group theory. The volume will interest group theorists, topologists, and experts in automata and language theory.
Download or read book Infinite Groups 1994 written by Francesco Giovanni and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-03-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Download or read book Infinite Groups written by Martyn R. Dixon and published by CRC Press. This book was released on 2022-12-30 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent times, group theory has found wider applications in various fields of algebra and mathematics in general. But in order to apply this or that result, you need to know about it, and such results are often diffuse and difficult to locate, necessitating that readers construct an extended search through multiple monographs, articles, and papers. Such readers must wade through the morass of concepts and auxiliary statements that are needed to understand the desired results, while it is initially unclear which of them are really needed and which ones can be dispensed with. A further difficulty that one may encounter might be concerned with the form or language in which a given result is presented. For example, if someone knows the basics of group theory, but does not know the theory of representations, and a group theoretical result is formulated in the language of representation theory, then that person is faced with the problem of translating this result into the language with which they are familiar, etc. Infinite Groups: A Roadmap to Some Classical Areas seeks to overcome this challenge. The book covers a broad swath of the theory of infinite groups, without giving proofs, but with all the concepts and auxiliary results necessary for understanding such results. In other words, this book is an extended directory, or a guide, to some of the more established areas of infinite groups. Features An excellent resource for a subject formerly lacking an accessible and in-depth reference Suitable for graduate students, PhD students, and researchers working in group theory Introduces the reader to the most important methods, ideas, approaches, and constructions in infinite group theory.
