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This two-volume book contains selected papers from the international conference 'Groups St Andrews 1997 in Bath'. The articles cover a wide spectrum of modern group theory. There are articles based on lecture courses given by five main speakers together with refereed survey and research articles contributed by other conference participants. Proceedings of earlier 'Groups St Andrews' conferences have had a major impact on the development of group theory and these volumes should be equally important.

Group theory --- Combinatorial group theory --- Combinatorial groups --- Groups, Combinatorial --- Combinatorial analysis

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A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.

Combinatorial group theory. --- Topological groups. --- Algebraic topology. --- Topology --- Groups, Topological --- Continuous groups --- Combinatorial groups --- Groups, Combinatorial --- Combinatorial analysis --- Group theory

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This volume presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Building on the foundations laid a quarter of a century ago in the volume Two-dimensional Homotopy and Combinatorial Group Theory (LMS 197), the editors here bring together much remarkable progress that has been obtained in the intervening years. And while the fundamental open questions, such as the Andrews-Curtis Conjecture and the Whitehead asphericity problem remain to be (fully) solved, this book will provide both students and experts with an overview of the state of the art and work in progress. Ample references are included to the LMS 197 volume, as well as a comprehensive bibliography bringin#g matters entirely up to date.

Homotopy theory. --- Combinatorial group theory. --- Low-dimensional topology. --- Topology, Low-dimensional --- Algebraic topology --- Manifolds (Mathematics) --- Combinatorial groups --- Groups, Combinatorial --- Combinatorial analysis --- Group theory --- Deformations, Continuous --- Topology

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This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dortmund and Ottawa in 2007. It contains high quality refereed articles developing new aspects of these modern and active fields in mathematics. It is also appropriate to advanced students interested in recent results at a research level.

Finite groups -- Congresses. --- Group theory -- Congresses. --- Mathematics. --- Combinatorial group theory --- Geometric group theory --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Combinatorial groups --- Groups, Combinatorial --- Group theory. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Math --- Science --- Group theory --- Combinatorial analysis

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Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.

Combinatorial group theory --- Finite groups --- Group theory --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Groups, Finite --- Modules (Algebra) --- Combinatorial groups --- Groups, Combinatorial --- Combinatorial analysis --- Data processing. --- Group theory - Data processing. --- Finite groups - Data processing. --- Combinatorial group theory - Data processing.