Analytic Pro-P Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analytic Pro-P Groups write by J. D. Dixon. This book was released on 2003-09-18. Analytic Pro-P Groups available in PDF, EPUB and Kindle. An up-to-date treatment of analytic pro-p groups for graduate students and researchers.
New Horizons in pro-p Groups
New Horizons in pro-p Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook New Horizons in pro-p Groups write by Marcus du Sautoy. This book was released on 2012-12-06. New Horizons in pro-p Groups available in PDF, EPUB and Kindle. A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed. Thus from one point of view, to study a pro-p group is the same as studying an infinite family of finite groups; but a pro-p group is also a compact topological group, and the compactness works its usual magic to bring 'infinite' problems down to manageable proportions. The p-adic integers appeared about a century ago, but the systematic study of pro-p groups in general is a fairly recent development. Although much has been dis covered, many avenues remain to be explored; the purpose of this book is to present a coherent account of the considerable achievements of the last several years, and to point the way forward. Thus our aim is both to stimulate research and to provide the comprehensive background on which that research must be based. The chapters cover a wide range. In order to ensure the most authoritative account, we have arranged for each chapter to be written by a leading contributor (or contributors) to the topic in question. Pro-p groups appear in several different, though sometimes overlapping, contexts.
p-Adic Lie Groups
p-Adic Lie Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook p-Adic Lie Groups write by Peter Schneider. This book was released on 2011-06-11. p-Adic Lie Groups available in PDF, EPUB and Kindle. Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings.
Linear Pro-p-Groups of Finite Width
Linear Pro-p-Groups of Finite Width - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear Pro-p-Groups of Finite Width write by Gundel Klaas. This book was released on 2006-11-14. Linear Pro-p-Groups of Finite Width available in PDF, EPUB and Kindle. The normal subgroup structure of maximal pro-p-subgroups of rational points of algebraic groups over the p-adics and their characteristic p analogues are investigated. These groups have finite width, i.e. the indices of the sucessive terms of the lower central series are bounded since they become periodic. The richness of the lattice of normal subgroups is studied by the notion of obliquity. All just infinite maximal groups with Lie algebras up to dimension 14 and most Chevalley groups and classical groups in characteristic 0 and p are covered. The methods use computers in small cases and are purely theoretical for the infinite series using root systems or orders with involutions.
Lectures on Profinite Topics in Group Theory
Lectures on Profinite Topics in Group Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Profinite Topics in Group Theory write by Benjamin Klopsch. This book was released on 2011-02-10. Lectures on Profinite Topics in Group Theory available in PDF, EPUB and Kindle. In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the theory of compact p-adic Lie groups. The second explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. The final chapter provides an overview of zeta functions associated to groups and rings. Derived from an LMS/EPSRC Short Course for graduate students, this book provides a concise introduction to a very active research area and assumes less prior knowledge than existing monographs or original research articles. Accessible to beginning graduate students in group theory, it will also appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.
