Related papers: Local indicability and commutator subgroups of Art…
In this note we give some new results concerning the subgroup commutativity degree of a finite group $G$. These are obtained by considering the minimum of subgroup commutativity degrees of all sections of $G$.
We find finite presentations for the automorphism group of the Artin pure braid group and the automorphism group of the pure braid group associated to the full monomial group.
We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.
We classify the finite connected-homogeneous digraphs, as well as the infinite such digraphs with precisely one end. This completes the classification of all the locally finite connected-homogeneous digraphs.
We define and give axioms for Garside and locally Garside categories. We give an application to Coxeter and Artin groups and Deligne-Lusztig varieties.
We find a condition on the underlying graph of an Artin group that fully determines if it is subgroup separable. As a consequence, an Artin group is subgroup separable if and only if it can be obtained from Artin groups of ranks at most 2…
We determine a classification of the endomorphisms of the Artin group of affine type $\tilde A_n$ for $n\ge 4$.
We prove that acylindrically hyperbolic groups are monotileable. That is, every finite subset of the group is contained in a finite tile. This provides many new examples of monotileable groups, and progress on the question of whether every…
We study a class of finite groups, called almost monomial groups, which generalize the class of monomial groups and it is connected with the theory of Artin L-functions. Our method of research is based on finding similarities with the…
We establish basic results on subrings of finite commutative rings and closely related rings. Among other applications we calculate the number of maximal subrings of a finite commutative local ring.
We give a complete list of the one-dimensional groups definable in algebraically closed valued fields and i the pseudo-local fields, up to a finite index subgroup and a quotient by a finite subgroup.
We investigate a family of (reducible) representations of Artin's braid groups corresponding to a specific solution to the Yang-Baxter equation. The images of the braid groups under these representations are finite groups, and we identify…
Abstract. We address the conjecture which states that an intersection of parabolic subgroups of an Artin-Tits group is a parabolic subgroup. We prove that the conjecture is equivalent to a, a priori, weaker conjecture. We also prove the…
We classify all non-degenerate skew-hermitian forms defined over certain local rings, not necessarily commutative, and study some of the fundamental properties of the associated unitary groups, including their orders when the ring in…
We prove several results on the model theory of Artin groups, focusing on Artin groups which are ``far from right-angled Artin groups''. The first result is that if $\mathcal{C}$ is a class of Artin groups whose irreducible components are…
In this article, we prove that a semidirect product of a locally finite group with a surjunctive group is also surjunctive. We also prove that a surjunctive-by-locally finite group is again surjunctive.
We show that the complex of parabolic subgroups associated to the Artin-Tits group of type $B$ is hyperbolic
A group G is a cn-group if for each subgroup H of G there exists a normal subgroup N of G such that the index of both H and N in HN is finite. The class of cn-groups contains properly the classes of core- finite groups and that of groups in…
In this article, we study the property of being equationally Artinian in groups. We prove that a finite extension of an equationally Artinian group is again equationally Artinian. We also show that a quotient of an equationally Artinian…
We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a…