Related papers: Abelian subgroups of two-dimensional Artin groups

The number of maximal abelian subgroups of a finite p-group is shown to be congruent to 1 modulo p.

We consider the lattice of subsemigroups of the general linear group over an Artinian ring containing the group of diagonal matrices and show that every such semigroup is actually a group.

We show that many $2$-dimensional Artin groups are residually finite. This includes $3$-generator Artin groups with labels $\geq 4$ except for $(2m+1, 4,4)$ for any $m\geq 2$. As a first step towards residual finiteness we show that these…

We obtain a classification of the finite two-generated cyclic-by-abelian groups of prime-power order. For that we associate to each such group $G$ a list $\inv(G)$ of numerical group invariants which determines the isomorphism type of $G$.…

We show that the intersection of parabolic subgroups of an even finitely generated FC-type Artin group is again a parabolic subgroup.

We prove that Artin groups from a class containing all large-type Artin groups are systolic. This provides a concise yet precise description of their geometry. Immediate consequences are new results concerning large-type Artin groups:…

We observe an inductive structure in a large class of Artin groups and exploit this information to deduce the Farrell-Jones isomorphism conjecture for several classes of Artin groups of finite real, complex and affine types.

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 every subgroup of it is either finitely generated abelian, or…

We consider several questions related to Pontryagin duality in the category of abelian pro-Lie groups.

We carry out the Cantor-Bendixson analysis of the space of all subgroups of any countable abelian group and we deduce a complete classification of such spaces up to homeomorphism.

We determine the structure of 2-blocks with minimal nonabelian defect groups, by making use of the classification of finite simple groups.

The present article continues the study of median groups initiated in [6, 9, 10]. Some classes of median groups are introduced and investigated with a stress upon the class of the so called A-groups which contains as remarkable subclasses…

We survey the analogy between Kleinian groups and subgroups of the mapping class group of a surface.

We construct examples of algebraic surfaces with interesting fundamental groups.

In this paper we characterize permutation groups that are automorphism groups of coloured graphs and digraphs and are abelian as abstract groups. This is done in terms of basic permutation group properties. Using Schur's classical…

A complete list of one dimensional groups definable in the p-adic numbers is given, up to a finite index subroup and a quotient by a finite subgroup.

We consider maximal abelian subalgebras of O_n which are invariant to the standard circle action.

We give some easy necessary and sufficient criteria for twists of abelian varieties by Artin representations to be simple.

Recently, right-angled Artin groups have attracted much attention in geometric group theory. They have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical complexes with a variety of applications.…

In this article we construct a piecewise Euclidean, non-positively curved 2-complex for the 3-generator Artin groups of large type. As a consequence we show that these groups are biautomatic. A slight modification of the proof shows that…