Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T16:01:35.722Z Has data issue: false hasContentIssue false
  • English
  • Français

NORMAL SUBGROUPS OF PROFINITE GROUPS OF FINITE COHOMOLOGICAL DIMENSION

Published online by Cambridge University Press:  29 March 2004

A. ENGLER ,
D. HARAN ,
D. KOCHLOUKOVA  and
P. A. ZALESSKII
A. ENGLER
Affiliation:
UNICAMP-IMECC, Caixa Postal 6065, 13083-970 Campinas, SP, Brazil
D. HARAN
Affiliation:
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
D. KOCHLOUKOVA
Affiliation:
UNICAMP-IMECC, Caixa Postal 6065, 13083-970 Campinas, SP, Brazil
P. A. ZALESSKII
Affiliation:
Department of Mathematics, University of Brasília, 70910-900 Brasília DF, Brazil
Get access

Abstract

A profinite group $G$ of finite cohomological dimension with (topologically) finitely generated closed normal subgroup $N$ is studied. If $G$ is pro-$p$ and $N$ is either free as a pro-$p$ group or a Poincaré group of dimension 2 or analytic pro-$p$, it is shown that $G/N$ has virtually finite cohomological dimension ${\rm cd}(G)\,{-}\,{\rm cd}(N)$. Some other cases when $G/N$ has virtually finite cohomological dimension are also considered.

If $G$ is profinite, the case of $N$ projective or the profinite completion of the fundamental group of a compact surface is considered.

Keywords

20E18 (primary)20E07 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 317 - 332
Copyright
The London Mathematical Society 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)