Related papers: Random Generation of Thompson's group $F$

We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in…

We solve the twisted conjugacy problem on Thompson's group F. We also exhibit orbit undecidable subgroups of Aut(F), and give a proof that Aut(F) and Aut_+(F) are orbit decidable provided a certain conjecture on Thompson's group T is true.…

Why does Zipf's law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous random group division: the elements can be…

We prove that there exists a group which is not finitely generated, but admits a minimal sofic shift. This answers a question of Doucha, Melleray and Tsankov. The group is of the form $(F_4 \times F_2) \rtimes F_{\infty}$. The construction…

Let G be a finite group and let k be a field of characteristic p. Given a finitely generated indecomposable non-projective kG-module M, we conjecture that if the Tate cohomology $\HHHH^*(G, M)$ of G with coefficients in M is finitely…

We propose a new approach to nondeterministic random number generation. In theory, the randomness originated from the uncorrelated nature of consecutive laser pulses with Poissonian photon number distribution and that of the consecutive…

We prove that there exists a finitely generated group that satisfies a group law with probability 1 but does not satisfy any group law. More precisely, we construct a finitely generated group G in which the probability that a random element…

We characterise the elements of the (maximum) idempotent generated subsemigroup of the Kauffman monoid in terms of combinatorial data associated to certain normal forms. We also calculate the smallest size of a generating set and idempotent…

We prove that random walks on Thompson's group $F$ driven by strictly non-degenerate finitely supported probability measures $\mu$ have a non-trivial Poisson boundary. The proof consists in an explicit construction of two different…

For k >= 1, let Torelli_g^1(k) be the k-th term in the Johnson filtration of the mapping class group of a genus g surface with one boundary component. We prove that for all k, there exists some G_k >= 0 such that Torelli_g^1(k) is generated…

We classify groups generated by powers of 2 Dehn twists which are 1) free or 2) have no ``unexpected'' reducible elements. We give some sufficient conditions in the case of groups generated by powers of more than two twists.

We show that one can naturally describe elements of R. Thompson's finitely presented infinite simple group $V$, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to…

We show that labelled Thompson groups and twisted Brin--Thompson groups are all acyclic. This allows us to prove several new embedding results for groups. First, every group of type $F_n$ embeds quasi-isometrically as a subgroup of an…

We address two questions of Simon Thomas. First, we show that for any n>2 one can find a four generated free subgroup of SLn(Z) which is profinitely dense. More generally, we show that an arithmetic group \Gamma which admits the congruence…

It is proved that all finitely generated subgroups of generalized free product of two groups are finitely separable provided that free factors have this property and amalgamated subgroups are normal in corresponding factors and satisfy the…

We prove that the braided Thompson's groups $V_{\rm br}$ and $F_{\rm br}$ are of type $F_\infty$, confirming a conjecture by John Meier. The proof involves showing that matching complexes of arcs on surfaces are highly connected. In an…

We investigate the cogrowth and distribution of geodesics in R. Thompson's group $F$.

Gowers has elegantly characterized the finite groups $G$ in which $A_1A_2A_3 = G$ for any positive density subsets $A_1,A_2,A_3$. This property, quasi-randomness, holds if and only if G does not admit a nontrivial irreducible representation…

We prove that for a number field $F$, the distribution of the points of a set $\Sigma \subset \mathbb{A}_F^n$ with a purely exponential parametrization, for example a set of matrices boundedly generated by semi-simple (diagonalizable)…

We improve some known estimates for the density of the Cayley graph of Thompson's group F in standard generators.