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Results tagged with gr.group-theory
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user 142651
Questions about the branch of algebra that deals with groups.
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 …
- 12.9k
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 …
- 63.9k
4
votes
0
answers
117
views
Amalgamated subgroup of an HNN extension finitely generated
Baumslag proved that if $G= A \ast_{C} B$ is an amalgamated free product where $A$ and $B$ are finitely presented, $G$ is finitely presented if and only if $C$ is finitely generated.
Similarly, by us …
- 321
2
votes
0
answers
238
views
Finite index subgroup of HNN extension
Let $GX$ be a tree group (a right-angled Artin group such that the graph is a tree), such that not all the subgroups of $GX$ are necessarily RAAGs, so the length of the tree is greater or equal than $ …
- 321