عنوان

New Horizons in pro-p Groups

(Number (ISBN

9781461213802

(Number (ISBN

9781461271222

Number

b402750

Title Proper

New Horizons in pro-p Groups

General Material Designation

[Book]

First Statement of Responsibility

edited by Marcus Sautoy, Dan Segal, Aner Shalev.

Place of Publication, Distribution, etc.

Boston, MA :

Name of Publisher, Distributor, etc.

Imprint: Birkhäuser,

Date of Publication, Distribution, etc.

2000.

Series Title

Progress in Mathematics ;

Volume Designation

184

Text of Note

1. Lie Methods in the Theory of pro-p Groups -- 2. On the Classification of p-groups and pro-p Groups -- 3. Pro-p Trees and Applications -- 4. Just Infinite Branch Groups -- 5. On Just Infinite Abstract and Profinite Groups -- 6. The Nottingham Group -- 7. On Groups Satisfying the Golod-Shafarevich Condition -- 8. Subgroup Growth in pro-p Groups -- 9. Zeta Functions of Groups -- 10. Where the Wild Things are: Ramification Groups and the Nottingham Group -- 11. p-adic Galois Representations and pro-p Galois Groups -- 12. Cohomology of p-adic Analytic Groups -- Appendix: Further Problems.

0

Text of Note

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.

International Standard Book Number

9781461271222

Title

Springer eBooks

Algebra.

Global analysis (Mathematics).

Group theory.

Mathematics.

Number theory.

Sautoy, Marcus.

Segal, Dan.

Shalev, Aner.

SpringerLink (Online service)

Date of Transaction

20190307160300.0

Electronic name

[Book]

Y