Automorphisms Of Finite Groups And Related Topics

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Automorphisms Of Finite Groups And Related Topics

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Author : Robert Sheehy
language : en
Publisher:
Release Date : 1994

Automorphisms Of Finite Groups And Related Topics written by Robert Sheehy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Group theory categories.

Automorphisms Of Riemann Surfaces Subgroups Of Mapping Class Groups And Related Topics

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Author : Aaron Wootton
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-03

Automorphisms Of Riemann Surfaces Subgroups Of Mapping Class Groups And Related Topics written by Aaron Wootton and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-03 with Mathematics categories.

Automorphism groups of Riemann surfaces have been widely studied for almost 150 years. This area has persisted in part because it has close ties to many other topics of interest such as number theory, graph theory, mapping class groups, and geometric and computational group theory. In recent years there has been a major revival in this area due in part to great advances in computer algebra systems and progress in finite group theory. This volume provides a concise but thorough introduction for newcomers to the area while at the same time highlighting new developments for established researchers. The volume starts with two expository articles. The first of these articles gives a historical perspective of the field with an emphasis on highly symmetric surfaces, such as Hurwitz surfaces. The second expository article focuses on the future of the field, outlining some of the more popular topics in recent years and providing 78 open research problems across all topics. The remaining articles showcase new developments in the area and have specifically been chosen to cover a variety of topics to illustrate the range of diversity within the field.

Automorphisms Of Finite Groups

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Author : Inder Bir Singh Passi
language : en
Publisher: Springer
Release Date : 2019-01-12

Automorphisms Of Finite Groups written by Inder Bir Singh Passi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-12 with Mathematics categories.

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.

Problems On Mapping Class Groups And Related Topics

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Author : Benson Farb
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-09-12

Problems On Mapping Class Groups And Related Topics written by Benson Farb and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-12 with Mathematics categories.

The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.

Vertex Operator Algebras Number Theory And Related Topics

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Author : Matthew Krauel
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-07-13

Vertex Operator Algebras Number Theory And Related Topics written by Matthew Krauel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-13 with Education categories.

This volume contains the proceedings of the International Conference on Vertex Operator Algebras, Number Theory, and Related Topics, held from June 11–15, 2018, at California State University, Sacramento, California. The mathematics of vertex operator algebras, vector-valued modular forms and finite group theory continues to provide a rich and vibrant landscape in mathematics and physics. The resurgence of moonshine related to the Mathieu group and other groups, the increasing role of algebraic geometry and the development of irrational vertex operator algebras are just a few of the exciting and active areas at present. The proceedings center around active research on vertex operator algebras and vector-valued modular forms and offer original contributions to the areas of vertex algebras and number theory, surveys on some of the most important topics relevant to these fields, introductions to new fields related to these and open problems from some of the leaders in these areas.

Finite Groups Of Automorphisms

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Author : Norman Biggs
language : en
Publisher: CUP Archive
Release Date : 1971-10-31

Finite Groups Of Automorphisms written by Norman Biggs and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-10-31 with Mathematics categories.

These are notes of lectures given at the University of Southampton, October-December 1969. The lectures were intended for research students working in areas related to the topics discussed, and for mathematicians working in other fields who were interested in hearing a survey of some current problems and their background. The character of the lectures has been retained by the inclusion of occasional 'philosophical' remarks, but the text has been kept free of references as far as possible.

Finite Groups

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Author : Daniel Gorenstein
language : en
Publisher: American Mathematical Society
Release Date : 2025-04-21

Finite Groups written by Daniel Gorenstein and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-21 with Mathematics categories.

…it is required reading for anyone who wishes to study the subject. —Mathematical Reviews The theory of finite simple groups enjoyed a period of spectacular activity in the 1950s and 1960s. The first edition of Gorenstein's book was published in 1968, at the time of some of the first major classification results. The second edition was published in 1980, when it was clear that the classification was understood and the proof was within reach. Gorenstein's treatment of the subject proved prescient, as many of the developments between the two editions could be seen as continuations of the material in the book. Even now, the book remains one of the best sources for an introduction to finite groups and the classification of the simple groups. Gorenstein's insight provides a guiding light through the many pages that have been dedicated to the proof.

Lie Algebras Vertex Operator Algebras And Related Topics

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Author : Katrina Barron
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-15

Lie Algebras Vertex Operator Algebras And Related Topics written by Katrina Barron and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-15 with Mathematics categories.

This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.

Topics On Riemann Surfaces And Fuchsian Groups

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Author : Emilio Bujalance García
language : en
Publisher: Cambridge University Press
Release Date : 2001-06-14

Topics On Riemann Surfaces And Fuchsian Groups written by Emilio Bujalance García and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-14 with Mathematics categories.

Introduction to Riemann surfaces for graduates and researchers, giving refreshingly new insights into the subject.

Topics In Dynamics And Ergodic Theory

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Author : Sergey Bezuglyi
language : en
Publisher: Cambridge University Press
Release Date : 2003-12-08

Topics In Dynamics And Ergodic Theory written by Sergey Bezuglyi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-08 with Mathematics categories.

This book contains a collection of survey papers by leading researchers in ergodic theory, low-dimensional and topological dynamics and it comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups.