9 papers
Classification of Artin groups admitting retractions onto their parabolic subgroups
Bruno Aarón Cisneros de la Cruz, MarÃa Cumplido, Islam Foniqi +1
We classify the Artin groups that admit retractions onto all of their parabolic subgroups. Our approach relies on a detailed analysis of triangular subgroups, with a key ingredient…
Magnus submonoids and membership problems in one-relator, surface and hyperbolic groups
Islam Foniqi, Robert D. Gray
Motivated by its applications to the word problem for one-relator inverse monoids, via results of Ivanov, Margolis, and Meakin (2001), we prove several decidability and undecidabil…
Conjugacy problem in T-RAAGs
Gemma Crowe, Islam Foniqi
In this paper, we construct an implementable algorithm which solves the conjugacy problem in twisted right-angled Artin groups (T-RAAGs). In certain cases, the complexity is known…
Droms Theorems for twisted right-angled Artin groups
Simone Blumer, Islam Foniqi, Claudio Quadrelli
We characterize twisted right-angled Artin groups whose finitely generated subgroups are also twisted right-angled Artin groups. Additionally, we give a classification of coherence…
On Subgroup Separability and Membership Problems in Twisted Right-Angled Artin Groups
Islam Foniqi
We characterize twisted right-angled Artin groups (T-RAAGs) that are subgroup separable using only their defining mixed graphs: such a group is subgroup separable if and only if th…
The submonoid and rational subset membership problems for Artin groups
Islam Foniqi
We demonstrate that the submonoid membership problem and the rational subset membership problem are equivalent in Artin groups. Both these problem are undecidable in a given Artin…