All Questions
Tagged with semigroups-and-monoids geometric-group-theory
8 questions
18
votes
1
answer
783
views
Are there any "simple" monoids with intermediate growth?
The discovery of the Grigorchuk group which has intermediate growth caused a number of other such groups to be found, but they are all fairly complicated, and as far as I know none of them are ...
- 1,947
7
votes
0
answers
260
views
Generating the monoid of injective endomorphisms of the free group
Let $F$ be the free group of rank $2$ (or any finite rank if this does not matter). The set of injective group endomorphisms $F\to F$ forms a monoid $M$ by compositions. Is there a simple looking set ...
- 121
6
votes
0
answers
183
views
Examples of groups with a positive homogeneous presentation without the Haagerup property or not of type $F_\infty$
I am looking for groups with a certain presentation that do not have the Haagerup property or are finitely presented but not of type $F_\infty$ (meaninig that for some $n\geq 3$ we cannot find any ...
- 61
6
votes
0
answers
572
views
Computing the pro-solvable closure of a finitely generated subgroup of a free group
The pro-solvable topology on a group $G$ is the unique group topology such that the set of normal subgroups $N\lhd G$ with $G/N$ a finite solvable group is a fundamental system of neighborhoods of the ...
- 38.6k
5
votes
1
answer
498
views
Percolation in Cayley graphs of semigroups.
Percolation in Cayley graphs of groups are studied by many researchers. There are also the concept Cayley graphs for semigroups. Are there any research about percolation in Cayley graphs for ...
- 6,201
4
votes
0
answers
72
views
When is the submonoid preserving a subspace finitely generated?
Let $T$ be a topological space with at least one open set whose closure is not open.
Let $G$ be a finitely generated group acting by homeomorphisms on $T$. Let $S\subset T$ be a subspace.
Under what ...
- 51
3
votes
1
answer
125
views
Quasi-isometries and E-unitary inverse semigroups
Let $S = \langle K\rangle$ be a finitely generated inverse semigroup, where $K \subset S$ is a fixed, finite and symmetric set of generators.
Preliminaries: Recall that we say that $s, t \in S$ are $\...
- 733
1
vote
0
answers
70
views
Another matrices for a semigroup with intermediate growth
Nathanson showed that the Okninski's semigroup $S$ of $2×2$ matrices which is generated by the set $H=\{A,B\}$, where
$
A=\begin{bmatrix}
1&1\\
0&1\\
\end{bmatrix}
,
B=\begin{bmatrix}
1&0\\...
- 883