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Results tagged with group-cohomology
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user 1463
In mathematics, group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of the group.
10
votes
Accepted
Finitely generated subgroups of a product of free groups
Regarding your first question, the answer is 'yes'. Consider an arbitrary direct product of free groups $\prod_\alpha F_\alpha$ and $H$ a finitely generated subgroup. Then $H$ is residually free. It …
- 25.2k
4
votes
Presentations of superperfect groups
For $M$ a closed, connected, orientable 3-manifold, it's well known that the existence of a Heegaard splitting for $M$ implies that the fundamental group $\pi_1M$ admits a balanced presentation (i.e. …
- 25.2k
18
votes
Accepted
Is there a finitely presented group with infinite homology over $\mathbb{Q}$?
Thompson's group F is an example. It's finitely presented and, according to this paper of Ken Brown, the integral homology is free abelian of rank 2 in every positive dimension.
- 25.2k