相关论文: Fast growth in Folner sets for Thompson's group F

Let $F(p)$, $p\ge2$ be the family of generalized Thompson's groups. Here F(2) is the famous Richard Thompson's group usually denoted by $F$. We find the growth rate of the monoid of positive words in $F(p)$ and show that it does not exceed…

We describe the results of some computational explorations in Thompson's group F. We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult…

We obtain a characterisation of confined subgroups of Thompson's group $F$. As a result, we deduce that orbital graph of a point under action of $F$ has uniformly subexponential growth if and only if this point is fixed by the commutator…

We have developed polynomial-time algorithms to generate terms of the cogrowth series for groups $\mathbb{Z}\wr \mathbb{Z},$ the lamplighter group, $(\mathbb{Z}\wr \mathbb{Z})\wr \mathbb{Z}$ and the Navas-Brin group $B.$ We have also given…

The purpose of this note is to prove that Richard Thompson's group F and variants of it studied by Ken Brown are not Kahler groups.

This article examines lower bounds for the representation growth of finitely generated (particularly profinite and pro-p) groups. It also considers the related question of understanding the maximal multiplicities of character degrees in…

The goal of this paper is to improve existing bounds for Fourier coefficients of higher genus Siegel modular forms of small weight.

In this paper, we will prove some sufficient conditions for the solvability of groups.

In this paper, the author (1) compares subnormal closures of finite sets in free groups; (2) proves that the exponential growth rate (e.g.r.), i.e., the limit of the n-th roots of g(n), where g(n) is the growth function of a subgroup H with…

The goal is to extend a non-standard amenability test for groups, based on random walks and superharmonic functions, to group actions on sets, and to apply it to Thompson's group F using certain properties of extensive amenability. While no…

We prove that Thompson's group F is not minimally almost convex with respect to any generating set which is a subset of the standard infinite generating set for F and which contains x_1. We use this to show that F is not almost convex with…

Intersection growth concerns the asymptotic behavior of the index of the intersection of all subgroups of a group that have index at most n. In this note we show that the intersection growth of some groups may not be a nicely behaved…

Let F be the Thompson's group. We study the structure of F-limit groups. Consider a sequence of groups marked by three elements, each isomorphic to F. Assume that the this sequence is convergent in the space of marked groups. We prove that…

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

In this short note, a bound on the word metric for Thompson's group V given by Birget in 2004 is improved to a new bound, which agrees with the known bounds for Thompson's groups F and T.

We consider random subgroups of Thompson's group $F$ with respect to two natural stratifications of the set of all $k$ generator subgroups. We find that the isomorphism classes of subgroups which occur with positive density are not the same…

In the paper, some lower bounds for polygamma functions are refined.

Recently we have shown a structure theorem for locally compact groups of polynomial growth. We give now some applications on various growth functions and relations to FC-G - series. In addition, we show some results on related classes of…

We reveal that Thompson's group $F$ has a quandle refinement, and we establish some essential results about the originating quandle.

We study some properties of the Cayley graph of the R.Thompson's group F in generators $x_0$, $x_1$. We show that the density of this graph, that is, the least upper bound of the average vertex degree of its finite subgraphs is at least 3.…