New Horizons in Pro-p Groups

The impetus for current research in pro-p groups comes from four main directions: from new applications in number theory, which continue to be a source of deep and challenging problems; from the traditional problem of classifying finite p-groups; from questions arising in infinite group theory; and finally, from the younger subject of 'profinite group theory'. A correspondingly diverse range of mathematical techniques is being successfully applied, leading to new results and pointing to exciting new directions of research. In this work important theoretical developments are carefully presented by leading mathematicians in the field, bringing the reader to the cutting edge of current research. With a systematic emphasis on the construction and examination of many classes of examples, the book presents a clear picture of the rich universe of pro-p groups, in its unity and diversity. Thirty open problems are discussed in the appendix. For graduate students and researchers in group theory, number theory, and algebra, this work will be an indispensable reference text and a rich source of promising avenues for further exploration.

ISBN 0817641718   Volumes 1 ISBN13 9780817641719 (What's this?)   Weight (grammes) 796 Publisher Birkhauser Boston Inc   Published in Secaucus Imprint Birkhauser Boston Inc   Series editor Oesterle, J., Oesterle, Joseph, Oesterle, J. Format Hardback   Series ISSN 184 Publication date 01 Jun 2000   Series title Progress in Mathematics Non-book description xiii, 423 p. :   Previous ISBN 9783764341718 Library of Congress 00023027   Height (mm) 234 DEWEY 512.2   Width (mm) 156 DEWEY edition DC21   Spine width (mm) 25 Pages 436   Academic level Undergraduate, Postgraduate

		Introduction
		Prerequisites and Notation
Ch. 1		Lie Methods in the Theory of pro-p Groups by Aner Shalev		1
Ch. 2		On the Classification of p-groups and pro-p Groups by C. R. Leedham-Green and S. McKay		55
Ch. 3		Pro-p Trees and Applications by Luis Ribes and Pavel Zalesskii		75
Ch. 4		Just Infinite Branch Groups by R. I. Grigorchuk		121
Ch. 5		On Just Infinite Abstract and Profinite Groups by John S. Wilson		181
Ch. 6		The Nottingham Group by Rachel Camina		205
Ch. 7		On Groups Satisfying the Golod-Shafarevich Condition by E. Zelmanov		223
Ch. 8		Subgroup Growth in pro-p Groups by Avinoam Mann		233
Ch. 9		Zeta Functions of Groups by Marcus du Sautoy and Dan Segal		249
Ch. 10		Where the Wild Things are: Ramification Groups and the Nottingham Group by Marcus du Sautoy and Ivan Fesenko		287
Ch. 11		p-adic Galois Representations and pro-p Galois Groups by Nigel Boston		329
Ch. 12		Cohomology of p-adic Analytic Groups by Peter Symonds and Thomas Weigel		349
		Appendix: Further Problems		411
		Index		417

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