Words: Notes on Verbal Width in Groups

by Dan Segal

Overview

After a forty-year lull, the study of word-values in groups has sprung back into life with some spectacular new results in finite group theory. These are largely motivated by applications to profinite groups, including the solution of an old problem of Serre. This book presents a comprehensive account of the known results, both old and new. The more elementary methods are developed from scratch, leading to self-contained proofs and improvements of some classic results about infinite soluble groups. This is followed by a detailed introduction to more advanced topics in finite group theory, and a full account of the applications to profinite groups. The author presents proofs of some very recent results and discusses open questions for further research. This self-contained account is accessible to research students, but will interest all research workers in group theory.

Product Details

ISBN-13:	9780521747660
Publisher:	Cambridge University Press
Publication date:	07/16/2009
Series:	London Mathematical Society Lecture Note Series , #361
Pages:	134
Product dimensions:	5.90(w) x 8.90(h) x 0.40(d)

About the Author

Dan Segal is Senior Research Fellow at All Souls College, Oxford, and Professor of Mathematics at the University of Oxford.

Table of Contents

Preface; 1. Generalities; 2. Verbally elliptic classes; 3. Words of infinite width; 4. Words and profinite groups; 5. Algebraic and analytic groups; Appendix; Bibliography; Index.

Editorial Reviews

"The monograph under review provides a concise, expository account of verbal width in groups, accessible to a broad readership. The book is a valuable contribution to this particular area of group theory. In addition to key results and techniques, it contains a fair number of exercises and it points toward a range of open problems."
Benjamin Klopsch, Mathematical Reviews

From the Publisher