Ischia Group Theory 2006

Author: Akbar Rhemtulla
Publisher: World Scientific
ISBN: 9812707352
Format: PDF, Kindle
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This volume contains a collection of research articles by leading experts in group theory and some accessible surveys of recent research in the area. Together they provide an overview of the diversity of themes and applications that interest group theorists today. Topics covered in this volume include: combinatorial group theory, varieties of groups, orderable groups, conjugacy classes, profinite groups, probabilistic methods in group theory, graphs connected with groups, subgroup structure, and saturated formations.

Profinite Groups

Author: John S. Wilson
Publisher: Oxford University Press
ISBN: 9780198500827
Format: PDF, ePub, Docs
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This is the first book to be dedicated entirely to profinite groups, an area of algebra with important links to number theory and other areas of mathematics. It provides a comprehensive overview of the subject; prerequisite knowledge is kept to a minimum, and several major theorems are presented in an accessible form. The book would provide a valuable introduction for postgraduate students, or form a useful reference for researchers in other areas. The first few chapters lay the foundations and explain the role of profinite groups in number theory. Later chapters explore various aspects of profinite groups in more detail; these contain accessible and lucid accounts of many major theorems. Prerequisites are kept to a minimum with the basic topological theory summarized in an introductory chapter.

New Directions in Locally Compact Groups

Author: Pierre-Emmanuel Caprace
Publisher: Cambridge University Press
ISBN: 1108349544
Format: PDF, Mobi
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This collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, p-adic Lie groups and the metric geometry of locally compact groups. Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail. An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis' theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice. An introduction to lattices, invariant random subgroups and L2-invariants, and a brief account of the Burger–Mozes construction of simple lattices are also included. A final chapter collects various problems suggesting future research directions.

The Structure of Groups of Prime Power Order

Author: Charles Richard Leedham-Green
Publisher: Clarendon Press
ISBN: 9780198535485
Format: PDF
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The coclass project (1980-1994) provided a new and powerful way to classify finite p-groups. This monograph gives a coherent account of the thinking out of which developed the philosophy that lead to this classification. The authors provide a careful summary and explanation of the many and difficult original research papers on the coclass conjecture and the structure theorem, thus elucidating the background research for those new to the area as well as for experienced researchers. The classification philosophy has lead to many new and challenging problems. Amongst those considered are problems about pro-p-groups, the Grigorchuk group, the Nottingham group as well as linear pro-p-groups. Throughout the book the authors have used a wide range of algebraic techniques and have developed from first principles, or from basic and well known results, the cohomology of groups, spectral sequences, and representation theory. This comprehensive and long-awaited survey of the recent and current research on the structure of finite p-groups will be an important reference for all group theorists.

Geometry Topology

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Format: PDF, ePub
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Fully refereed international journal dealing with all aspects of geometry and topology and their applications.