Normal Subgroups of Profinite Groups of Finite Cohomological Dimension |
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Authors: | Engler A; Haran D; Kochloukova D; Zalesskii P A |
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Institution: | UNICAMP-IMECC Caixa Postal 6065, 13083-970 Campinas, SP, Brazil
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University Ramat Aviv, Tel Aviv 69978, Israel
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 Gis pro-p and N is either free as a pro-p group or a Poincarégroup of dimension 2 or analytic pro-p, it is shown that G/Nhas virtually finite cohomological dimension cd(G)cd(N).Some other cases when G/N has virtually finite cohomologicaldimension are also considered. If G is profinite, the case of N projective or the profinitecompletion of the fundamental group of a compact surface isconsidered. |
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