2 citations · 4 across the 14 of their papers we have counts for
6 papers · 1 filter
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…
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 -finite. The proo…
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…
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…
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 , or it is virtually solvable. This paper considers two decision…
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…