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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
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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

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