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Classification of Artin groups admitting retractions onto their parabolic subgroups
Bruno Aarón Cisneros de la Cruz, María 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…
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…
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…
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…
On Artin groups admitting retractions to parabolic subgroups
Bruno Aaron Cisneros de la Cruz, María Cumplido, Islam Foniqi
We generalize the retractions to standard parabolic subgroups for even Artin groups to FC-type Artin groups and other more general families. We prove that these retractions uniquel…
Twisted right-angled Artin groups
Islam Foniqi
We present a complete rewriting system for twisted right-angled Artin groups. Utilizing the normal form coming from the rewriting system, we provide applications that illustrate di…
Subgroups of even Artin groups of FC-type
Yago Antolín, Islam Foniqi
We prove a Tits alternative theorem for subgroups of finitely generated even Artin groups of FC type (EAFC groups), stating that there exists a finite index subgroup such that ever…
Membership problems for positive one-relator groups and one-relation monoids
Islam Foniqi, Robert D. Gray, Carl-Fredrik Nyberg-Brodda
Motivated by approaches to the word problem for one-relation monoids arising from work of Adian and Oganesian (1987), Guba (1997), and Ivanov, Margolis and Meakin (2001), we study…
Intersection of parabolic subgroups in even Artin groups of FC-type
Yago Antolín, Islam Foniqi
We show that the intersection of parabolic subgroups of an even finitely generated FC-type Artin group is again a parabolic subgroup.
Geodesic Growth of some 3-dimensional RACGs
Yago Antolín, Islam Foniqi
We give explicit formulas for the geodesic growth series of a Right Angled Coxeter Group (RACG) based on a link-regular graph that is 4-clique free, i.e. without tetrahedrons