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Results tagged with group-cohomology
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user 142651
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.
7
votes
Accepted
Extension of $FP_{n}$ group
If $0\to A \to B \to C\to 0$ is a short exact sequence of groups and $A$, $C$ are of type $FP_{n}$, then so is $B$. Reference: Proposition 2.2 in Homological finiteness properties of fibre products by …
- 321
5
votes
1
answer
326
views
Extension of $FP_{n}$ group
I am reading a paper (Finitely presented residually free groups by Bridson, Howie, Miller III, and Short, Theorem 5.2) where they write the following:
Since $S_{0}$ is a group of type $FP_{n}(\mathbb …
- 321
4
votes
1
answer
167
views
When does $FP_n(R)$ imply $F_n$?
It is known that if a group $G$ is of type $F_2$ (finitely presented) and of type $FP_n(\mathbb{Z})$, then $G$ is of type $F_n$.
However, is this true also for other rings which are not $\mathbb{Z}$? …
- 321