Words
Notes on Verbal Width in Groups

Explores fundamental questions about the behaviour of word-values in groups.

Dan Segal (Author)

9780521747660, Cambridge University Press

Paperback, published 16 July 2009

134 pages, 30 exercises
22.9 x 15.2 x 0.8 cm, 0.21 kg

"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

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.

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.

Subject Areas: Algebra [PBF]