Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus


IMPACT FACTOR 2018: 0.470
5-year IMPACT FACTOR: 0.520

CiteScore 2018: 0.53

SCImago Journal Rank (SJR) 2018: 0.566
Source Normalized Impact per Paper (SNIP) 2018: 1.047

Mathematical Citation Quotient (MCQ) 2018: 0.48

Online
ISSN
1435-4446
See all formats and pricing
More options …
Volume 12, Issue 5

Issues

Analytic pro-p groups of small dimensions

Jon González-Sánchez
  • Departmento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Avda. de los Castros, E-39071 Santander, Spain. E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Benjamin Klopsch
  • Department of Mathematics, Royal Holloway, University of London, Egham TW20 0EX, United Kingdom. E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2009-04-17 | DOI: https://doi.org/10.1515/JGT.2009.006

Abstract

According to Lazard, every p-adic Lie group contains an open pro-p subgroup which is saturable. This can be regarded as the starting point of p-adic Lie theory, as one can naturally associate to every saturable pro-p group G a Lie lattice L(G) over the p-adic integers.

Essential features of saturable pro-p groups include that they are torsion-free and p-adic analytic. In the present paper we prove a converse result in small dimensions: every torsion-free p-adic analytic pro-p group of dimension less than p is saturable.

This leads to useful consequences and interesting questions. For instance, we give an effective classification of 3-dimensional soluble torsion-free p-adic analytic pro-p groups for p > 3. Our approach via Lie theory is comparable with the use of Lazard's correspondence in the classification of finite p-groups of small order.

About the article

Received: 2007-11-15

Revised: 2008-06-18

Published Online: 2009-04-17

Published in Print: 2009-09-01


Citation Information: Journal of Group Theory, Volume 12, Issue 5, Pages 711–734, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/JGT.2009.006.

Export Citation

© de Gruyter 2009.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[2]
Daniel Delbourgo and Qin Chao
Annales mathématiques du Québec, 2018
[3]
Daniel Delbourgo and Antonio Lei
The Ramanujan Journal, 2017, Volume 43, Number 1, Page 29
[4]
Nir Avni, Benjamin Klopsch, Uri Onn, and Christopher Voll
Geometric and Functional Analysis, 2016, Volume 26, Number 1, Page 67
[5]
Benjamin Klopsch and Ilir Snopce
Journal of Algebra, 2011, Volume 331, Number 1, Page 263
[6]
Jon González-Sánchez
Communications in Algebra, 2009, Volume 37, Number 12, Page 4476
[7]
Jon González-Sánchez and Alejandro P. Nicolas
Journal of Algebra, 2011, Volume 334, Number 1, Page 54

Comments (0)

Please log in or register to comment.
Log in