TY - JOUR
T1 - Normal subgroups of profinite groups of finite cohomological dimension
AU - Engler, A.
AU - Haran, D.
AU - Kochloukova, D.
AU - Zalesskii, P. A.
N1 - Funding Information:
The first, third and fourth authors were partially supported by research grants from CNPq, Brazil. The second author was partially supported by a grant from FAPESP, Brazil.
PY - 2004/4
Y1 - 2004/4
N2 - 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 cd(G) - 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.
AB - 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 cd(G) - 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.
UR - http://www.scopus.com/inward/record.url?scp=2442467949&partnerID=8YFLogxK
U2 - 10.1112/S0024610703005003
DO - 10.1112/S0024610703005003
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AN - SCOPUS:2442467949
SN - 0024-6107
VL - 69
SP - 317
EP - 332
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
IS - 2
ER -