Gili Golan

activity

20132026

most citedThe generation problem in Thompson group

F

12 citations · 35 across the 16 of their papers we have counts for

collaborators

20 papers

math.GR2026

Finiteness properties of closed subgroups of Thompson's group $F$

Gili Golan

A subgroup $H$ of Thompson's group $F$ is closed if every piecewise- $H$ function in $F$ belongs to $H$ . Prominent examples of closed subgroups are the maximal subgroups of infinite…

math.GR2026

Every copy of Thompson's group $F$ in $F$ is undistorted

Gili Golan

Thompson's group $F$ is the group of all piecewise-linear homeomorphisms of the unit interval whose breakpoints are dyadic and whose slopes are integer powers of $2$ . If $H$ is a f…

math.GR2026

Irreducible fast sets of bump homeomorphisms generate copies of Thompson's groups $F_{n}$

Gili Golan

A homeomorphism of an interval is a positive bump if its support is a single open interval on which it moves every point to the right. Choosing a fundamental domain $[m, b (m))$ for…

math.GR2026

Higman--Thompson groups $F_{n}$ all the way down

Gili Golan

We prove that for every $n \geq 2$ the Higman--Thompson group $F_{n}$ has a maximal subgroup of infinite index isomorphic to itself. In fact, we construct a chain of subgroups $F_n=H_0…

math.GR2026

On the generation problem in Thompson's groups $F_{n}$

Gili Golan, Eytan Sapir

We study the generation problem in the Higman-Thompson groups $F_{n}$ via the core and closure of subgroups of $F_{n}$ and associated automata. We give sufficient conditions for a subs…

math.HO2024

Remembering Mark Sapir

Jean-Camille Birget, Gili Golan, Alexander Olshanskii +1

This memorial article for Mark Sapir provides a brief overview of his life and career. Among his many contributions we highlight two of his most celebrated achievements: his ground…

math.GR2024

The "spread" of Thompson's group $F$

Gili Golan

Recall that a group $G$ is said to be $\frac{3}{2}$ -generated if every non-trivial element $g \in G$ has a co-generator in $G$ (i.e., an element which together with $g$ generates $G…

math.GR2022

Thompson's group $F$ is almost $\frac{3}{2}$ -generated

Gili Golan

Recall that a group $G$ is said to be $\frac{3}{2}$ -generated if every non-trivial element of $G$ belongs to a generating pair of $G$ . Thompson's group $V$ was proved to be $\frac{…

math.GR2018

Autostackability of Thompson's group $F$

Nathan Corwin, Gili Golan, Susan Hermiller +2

The word problem for Thompson's group $F$ has a solution, but it remains unknown whether $F$ is automatic or has a finite or regular convergent (terminating and confluent) rewritin…

math.GR2017★ 1 cited

Divergence of Thompson groups

Gili Golan, Mark Sapir

We prove that R. Thompson groups F, T, V have linear divergence functions.

math.GR2016★ 1 cited

Invariable generation of Thompson groups

Tsachik Gelander, Gili Golan, Kate Juschenko

A subset $S$ of a group $G$ invariably generates $G$ if $G = ⟨ s^{g (s)} ∣ s \in S ⟩$ for every choice of $g (s) \in G, s \in S$ . We say that a group $G$ is invariably gener…

math.CO2016★ 5 cited

Nonempty intersection of longest paths in $2 K_{2}$ -free graphs

Gili Golan, Songling Shan

In 1966, Gallai asked whether all longest paths in a connected graph share a common vertex. Counterexamples indicate that this is not true in general. However, Gallai's question is…

math.GR2016★ 12 cited

The generation problem in Thompson group $F$

Gili Golan

We show that the generation problem in Thompson group $F$ is decidable, i.e., there is an algorithm which decides if a finite set of elements of $F$ generates the whole $F$ . The al…

math.GR2016

On the stabilizers of finite sets of numbers in the R. Thompson group $F$

Gili Golan, Mark Sapir

We study subgroups $H_{U}$ of the R. Thompson group $F$ which are stabilizers of finite sets $U$ of numbers in the interval $(0, 1)$ . We describe the algebraic structure of $H_{U}$ and…

math.GR2015

On subgroups of R. Thompson's group $F$

Gili Golan, Mark Sapir

We provide two ways to show that the R. Thompson group $F$ has maximal subgroups of infinite index which do not fix any number in the unit interval under the natural action of $F$ …

cs.IT2015

The Gaussian Channel with Noisy Feedback: Improving Reliability via Interaction

Assaf Ben-Yishai, Ofer Shayevitz

Consider a pair of terminals connected by two independent (feedforward and feedback) Additive White Gaussian Noise (AWGN) channels, and limited by individual power constraints. The…

math.GR2014

Tarski numbers of group actions

Gili Golan

The Tarski number of an action of a group G on a set X is the minimal number of pieces in a paradoxical decomposition of it. For any k>3 we construct a faithful transitive action o…

math.GR2014★ 1 cited

Groups with Tarski number 5

Gili Golan

The Tarski number of a non-amenable group G is the minimal number of pieces in a paradoxical decomposition of G. Until now the only numbers which were known to be Tarski numbers of…

math.GR2014★ 10 cited

The Tarski numbers of groups

Mikhail Ershov, Gili Golan, Mark Sapir

The Tarski number of a non-amenable group G is the minimal number of pieces in a paradoxical decomposition of G. In this paper we investigate how Tarski numbers may change under va…

math.CO2013★ 5 cited

Hindman's Coloring Theorem in arbitrary semigroups

Gili Golan, Boaz Tsaban

Hindman's Theorem asserts that, for each finite coloring of the natural numbers, there are distinct natural numbers $a_{1}, a_{2}, \dots$ such that all of the sums $a_{i_1}+a_{i_2}+\dots…

Finiteness properties of closed subgroups of Thompson's group F

Every copy of Thompson's group F in F is undistorted

Irreducible fast sets of bump homeomorphisms generate copies of Thompson's groups Fn​

Higman--Thompson groups Fn​ all the way down

On the generation problem in Thompson's groups Fn​

Remembering Mark Sapir

The "spread" of Thompson's group F

Thompson's group F is almost 23​-generated

Autostackability of Thompson's group F

Divergence of Thompson groups

Invariable generation of Thompson groups

Nonempty intersection of longest paths in 2K2​-free graphs

The generation problem in Thompson group F

On the stabilizers of finite sets of numbers in the R. Thompson group F

On subgroups of R. Thompson's group F

The Gaussian Channel with Noisy Feedback: Improving Reliability via Interaction

Tarski numbers of group actions

Groups with Tarski number 5

The Tarski numbers of groups

Hindman's Coloring Theorem in arbitrary semigroups

Finiteness properties of closed subgroups of Thompson's group $F$

Every copy of Thompson's group $F$ in $F$ is undistorted

Irreducible fast sets of bump homeomorphisms generate copies of Thompson's groups $F_{n}$

Higman--Thompson groups $F_{n}$ all the way down

On the generation problem in Thompson's groups $F_{n}$

The "spread" of Thompson's group $F$

Thompson's group $F$ is almost $\frac{3}{2}$ -generated

Autostackability of Thompson's group $F$

Nonempty intersection of longest paths in $2 K_{2}$ -free graphs

The generation problem in Thompson group $F$

On the stabilizers of finite sets of numbers in the R. Thompson group $F$

On subgroups of R. Thompson's group $F$