Let 1 --> N --> G --> G/N --> 1 be a short exact sequence of profinite groups, and let p be a prime number. We prove that if G is of finite cohomological p-dimension n := cd(p)(G) < infinity and if the order of H-k(N, F-p) is finite for k := cd(p)(N), the virtual cohomological p-dimension of G/N equals n - k. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.
Weigel, T., Zalesskii, P. (2004). Profinite groups of finite cohomological dimension. COMPTES RENDUS MATHÉMATIQUE, 338(5), 353-358 [10.1016/j.crma.2003.12.022].
Profinite groups of finite cohomological dimension
WEIGEL, THOMAS STEFAN;
2004
Abstract
Let 1 --> N --> G --> G/N --> 1 be a short exact sequence of profinite groups, and let p be a prime number. We prove that if G is of finite cohomological p-dimension n := cd(p)(G) < infinity and if the order of H-k(N, F-p) is finite for k := cd(p)(N), the virtual cohomological p-dimension of G/N equals n - k. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.
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