The cohomological restriction map and FP-infinity groups.

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Let G be a group and let H be a subgroup of G of finite index. As a result of Quillen's Theorem we know that if G is finite, then the restriction map from the cohomology ring of G to that of H has a finitely generated kernel. Following Bartholdi, we ask whether this is true for an arbitrary group G. We will show that this is true in case the group G is of type FP∞ and has virtual finite cohomological dimension, and we will give two counterexamples for the general case, one in which G is not finitely generated, and one in which the group G is an FP∞ group.
Original languageEnglish
Pages (from-to)1101-1114
JournalBulletin of the London Mathematical Society
Issue number6
Early online date5 Oct 2010
Publication statusPublished - Dec 2010


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