Automorphisms of a system survey its symmetry and appear nearly in all mathematical branches, such as those of algebra, combinatorics, geometry, … and theoretical physics or chemistry. The main motivation of this book is to present a systemically introduction to automorphism groups on algebra, graphs, maps, i.e., graphs on surfaces and geometrical structures with applications. Topics covered in this book include elementary groups, symmetric graphs, graphs on surfaces, regular maps, lifted automorphisms of graphs or maps, automorphisms of maps underlying a graph with applications to map enumeration, isometries on Smarandache geometry and CC conjecture, etc., which is suitable as a textbook for graduate students, and also a valuable reference for researchers in group action, graphs with groups, combinatorics with enumeration,
Smarandache multispaces, particularly, Smarandache geometry with applications.

Automorphisms of a system survey its symmetry and appear nearly in all mathematical branches, such as those of algebra, combinatorics, geometry, … and theoretical physics or chemistry. The main motivation of this book is to present a systemically introduction to automorphism groups on algebra, graphs, maps, i.e., graphs on surfaces and geometrical structures with applications. Topics covered in this book include elementary groups, symmetric graphs, graphs on surfaces, regular maps, lifted automorphisms of graphs or maps, automorphisms of maps underlying a graph with applications to map enumeration, isometries on Smarandache geometry and CC conjecture, etc., which is suitable as a textbook for graduate students, and also a valuable reference for researchers in group action, graphs with groups, combinatorics with enumeration,
Smarandache multispaces, particularly, Smarandache geometry with applications.

Automorphisms of a system survey its symmetry and appear nearly in all mathematical branches, such as those of algebra, combinatorics, geometry, …and theoretical physics or chemistry. The main motivation of this book is to present a systemically introduction to automorphism groups on algebra, graphs, maps, i.e., graphs on surfaces and geometrical structures with applications. Topics covered in this book include elementary groups, symmetric graphs, graphs on surfaces, regular maps, lifted automorphisms of graphs or maps, automorphisms of maps underlying a graph with applications to map enumeration, isometries on Smarandache geometry and CC conjecture, etc., which is suitable as a textbook for graduate students, and also a valuable reference for researchers in group action, graphs with groups, combinatorics with enumeration,
Smarandache multispaces, particularly, Smarandache geometry with applications.

Automorphisms of a system survey its symmetry and appear nearly in all mathematical branches, such as those of algebra, combinatorics, geometry, …and theoretical physics or chemistry. The main motivation of this book is to present a systemically introduction to automorphism groups on algebra, graphs, maps, i.e., graphs on surfaces and geometrical structures with applications. Topics covered in this book include elementary groups, symmetric graphs, graphs on surfaces, regular maps, lifted automorphisms of graphs or maps, automorphisms of maps underlying a graph with applications to map enumeration, isometries on Smarandache geometry and CC conjecture, etc., which is suitable as a textbook for graduate students, and also a valuable reference for researchers in group action, graphs with groups, combinatorics with enumeration,
Smarandache multispaces, particularly, Smarandache geometry with applications.

This book describes the recent development in the structure theory of von Neumann algebras and their automorphism groups. It can be viewed as a guided tour to the state of the art.

Motivated by some notorious open problems, such as the Jacobian conjecture and the tame generators problem, the subject of polynomial automorphisms has become a rapidly growing field of interest. This book, the first in the field, collects many of the results scattered throughout the literature. It introduces the reader to a fascinating subject and brings him to the forefront of research in this area. Some of the topics treated are invertibility criteria, face polynomials, the tame generators problem, the cancellation problem, exotic spaces, DNA for polynomial automorphisms, the Abhyankar-Moh theorem, stabilization methods, dynamical systems, the Markus-Yamabe conjecture, group actions, Hilbert's 14th problem, various linearization problems and the Jacobian conjecture. The work is essentially self-contained and aimed at the level of beginning graduate students. Exercises are included at the end of each section. At the end of the book there are appendices to cover used material from algebra, algebraic geometry, D-modules and Gröbner basis theory. A long list of ''strong'' examples and an extensive bibliography conclude the book.

This book, which grew out of Steven Bleiler's lecture notes from a course given by Andrew Casson at the University of Texas, is designed to serve as an introduction to the applications of hyperbolic geometry to low dimensional topology. In particular it provides a concise exposition of the work of Neilsen and Thurston on the automorphisms of surfaces. The reader requires only an understanding of basic topology and linear algebra, while the early chapters on hyperbolic geometry and geometric structures on surfaces can profitably be read by anyone with a knowledge of standard Euclidean geometry desiring to learn more abour other 'geometric structures'.

This volume provides in-depth coverage of selected areas of graph theory, with a main focus on symmetry properties of graphs. Standard topics on graph automorphisms are presented early on, while in later chapters, more specialized topics are tackled--such as graphical regular representations and pseudosimilarity. The final four chapters are devoted to the reconstruction problem; special emphasis is given to those results that involve the symmetry of graphs. Students who master the contents of this book will be well prepared for current research in many aspects of the theory of graph automorphisms and the reconstruction problem.

This book provides a detailed but concise account of the theory of structure of finite p-groups admitting p-automorphisms with few fixed points. The relevant preliminary material on Lie rings is introduced and the main theorems of the book on the solubility of finite p-groups are then presented. The proofs involve notions such as viewing automorphisms as linear transformations, associated Lie rings, powerful p-groups, and the correspondences of A.I. Mal'cev and M. Lazard given by the Baker-Hausdorff formula. Many exercises are included. This book is suitable for graduate students and researchers working in the fields of group theory and Lie rings.

The theory of automorphisms and derivations of associative rings is a direct descendant of the development of classical Galois theory and the theory of invariants. This volume presents a comprehensive overview of the methods and results of that theory, which has been greatly enriched during the last twenty years. Some of the material included appears for the first time. Among the problems discussed in this book are the following: construction of a Galois theory for prime and semiprime rings and its application to domains and free algebras; investigation of the problems of the algebraic dependence of automorphisms and derivations; studies of the fixed rings for finite groups and rings of constants for differential Lie algebras acting on the rings; non-commutative invariants of linear groups; theorems of finite groups acting on modular lattices; actions of Hopf algebras. The monograph is meant for specialists in algebra, but it can also be useful for a wider range of mathematicians. The inclusions in the book of the latest achievements on the structural theory of rings with generalized identities makes it desirable reading for graduate students as well.