Corentin Bodart

activity

20222026

most citedMembership problems in nilpotent groups

2 citations · 4 across the 14 of their papers we have counts for

collaborators

16 papers

math.GR2026

Subgroup and Submonoid Membership in the lampshuffler of $Z$

Corentin Bodart, Ruiwen Dong

The lampshuffler group of $Z$ is the semidirect product $FSym (Z) ⋊ Z$ , which consists of all permutations of $Z$ that act a…

math.GR2026

Green languages and growth of free inverse monoids

Corentin Bodart, André Carvalho, Ana-Catarina C. Monteiro +1

Motivated by recent work on conjugacy languages in groups, we introduce a general framework for studying \emph{languages of representatives} associated to equivalence relations on…

math.GR2026

A graph-theoretical characterisation of subgroups of Thompson's group $V$

Corentin Bodart, Daniele D'Angeli, Davide Perego +1

We prove a graph-theoretical characterisation of finitely generated subgroups of Thompson's group $V$ : a finitely generated group embeds in $V$ if and only if it admits a faithful…

math.GR2026

Period growth and co-context-free groups

Alex Bishop, Corentin Bodart, Letizia Issini +1

We study period growth in co-context-free groups, giving general results and looking at specific examples such as Thompson groups $T$ and $V$ and the Houghton groups $H_{m}$ . Along t…

math.GR2025

Groups with a finite Busemann boundary are virtually cyclic

Corentin Bodart, Liran Ron-George, Ariel Yadin

This note is a continuation of the study of the relationship between the geometry of Cayley graphs and the size of its metric-functional boundary. We show that, if there exists a C…

math.GR2025

Twisted commutativity and conjugacy ratio in groups

Laura Ciobanu, Gemma Crowe, Pieter Senden +1

In this paper we introduce and study the degree of twisted commutativity and the twisted conjugacy ratio of a finitely generated group $G$ . The degree of twisted commutativity $\ma…

math.GR2025

On finite extensions of lamplighter groups

Corentin Bodart

We study a family of groups consisting of the simplest extensions of lamplighter groups. We use these groups to answer multiple open questions in combinatorial group theory, provid…

math.GR2024

Ordering groups and the Identity Problem

Corentin Bodart, Laura Ciobanu, George Metcalfe

In this paper, the Identity Problem for certain groups, which asks if the subsemigroup generated by a given finite set of elements contains the identity element, is related to prob…

math.GR2024

A virtually nilpotent group whose Green series is not D-finite

Corentin Bodart

We provide the first example of virtually nilpotent group, with a specific generating set, for which the Green series (sometimes called cogrowth series) is not $D$ -finite. The proo…

math.GR2024

Horofunctions on the Heisenberg and Cartan groups

Corentin Bodart, Kenshiro Tashiro

We study the horofunction boundary of finitely generated nilpotent groups, and the natural group action on it. More specifically, we prove the followings results: For discrete Heis…

math.GR2024

Finitely presented groups with transcendental spectral radius

Corentin Bodart, Denis Osin

We provide examples of groups with transcendental spectral radius: We first construct finitely presented examples, using links between decidability of the Word Problem and semi-com…

math.GR2024

The Identity Problem in virtually solvable matrix groups over algebraic numbers

Corentin Bodart, Ruiwen Dong

The Tits alternative states that a finitely generated matrix group either contains a nonabelian free subgroup $F_{2}$ , or it is virtually solvable. This paper considers two decision…

math.GR2024★ 2 cited

Membership problems in nilpotent groups

Corentin Bodart

We study both the Submonoid Membership problem and the Rational Subset Membership problem in finitely generated nilpotent groups. We give two reductions with important applications…

math.GR2023★ 1 cited

Intermediate geodesic growth in virtually nilpotent groups

Corentin Bodart

We give a criterion on pairs $(G, S)$ - where $G$ is a virtually $s$ -step nilpotent group and $S$ is a finite generating set - saying whether the geodesic growth is exponential or s…

math.GR2022

Dead ends and rationality of complete growth series

Pierre Alderic Bagnoud, Corentin Bodart

The complete growth series of a finitely generated group is given by $\sum_{n \geq 0} A_{n} s^{n}$ , where $A_{n}$ is the sum of elements of length $n$ in the group semiring. We study the $\…

math.GR2022★ 1 cited

Rational cross-sections, bounded generation and orders on groups

Corentin Bodart

We provide new examples of groups without rational cross-sections (also called regular normal forms), using connections with bounded generation and rational orders on groups. Speci…

Subgroup and Submonoid Membership in the lampshuffler of Z

Green languages and growth of free inverse monoids

A graph-theoretical characterisation of subgroups of Thompson's group V

Period growth and co-context-free groups

Groups with a finite Busemann boundary are virtually cyclic

Twisted commutativity and conjugacy ratio in groups

On finite extensions of lamplighter groups

Ordering groups and the Identity Problem

A virtually nilpotent group whose Green series is not D-finite

Horofunctions on the Heisenberg and Cartan groups

Finitely presented groups with transcendental spectral radius

The Identity Problem in virtually solvable matrix groups over algebraic numbers

Membership problems in nilpotent groups

Intermediate geodesic growth in virtually nilpotent groups

Dead ends and rationality of complete growth series

Rational cross-sections, bounded generation and orders on groups

Subgroup and Submonoid Membership in the lampshuffler of $Z$

A graph-theoretical characterisation of subgroups of Thompson's group $V$