Add to ORKGWe show that two-dimensional Artin groups satisfy a strengthening of the Tits alternative: their subgroups either contain a non-abelian free group or are virtually free abelian of rank at most $2$. When in addition the associated Coxeter group is hyperbolic, we answer in the affirmative a question of Wise on the subgroups generated by large powers of two elements: given any two elements $a, b$ of a two-dimensional Artin group of hyperbolic type, there exists an integer $n\geq 1$ such that $a^n$ and $b^n$ either commute or generate a non-abelian free subgroup.Comment: 24 pages, 7 figures. Final version accepted for publicatio
Rosenberger’s conjecture is proved for groups T(2,l,2,R) with l=6, 12, 30, 60 and some special group...
26 pages, 2 figuresLet $G=G_1\ast\dots\ast G_k\ast F$ be a countable group which splits as a free pr...
We conjecture that the word problem of Artin-Tits groups can be solved without introducing trivial f...
A theorem of Cantat and Urech says that an analog of the classical Tits alternative holds for the gr...
Pride groups, or ?groups given by presentations in which each defining relator involves at most two ...
We extend previous results by Cumplido, Martin and Vaskou on parabolic subgroups of large-type Artin...
The class of groups defined by periodic paired relations, as introduced by Vinberg, includes the gen...
. The Tits conjecture claims that the subgroup generated by the squares of the standard generators o...
One says that the Tits alternative holds for a finitely generated group G if G contains either a non...
Artin groups, also called Artin-Tits groups, have been widely studied since their introduction by Ti...
We show the existence of several new infinite families of polynomially-growing automorphisms of free...
14 pagesA theorem of Cantat and Urech says that an analog of the classical Tits alternative holds fo...
We show that for every integer $d$, there is a constant $N(d)$ such that if $K$ is any field and $F$...
This paper is a short survey on four basic questions on Artin-Tits groups: the torsion, the center, ...
Tits proved that if G is a finitely generated linear group then G contains either a non abelian fre...
Rosenberger’s conjecture is proved for groups T(2,l,2,R) with l=6, 12, 30, 60 and some special group...
26 pages, 2 figuresLet $G=G_1\ast\dots\ast G_k\ast F$ be a countable group which splits as a free pr...
We conjecture that the word problem of Artin-Tits groups can be solved without introducing trivial f...
A theorem of Cantat and Urech says that an analog of the classical Tits alternative holds for the gr...
Pride groups, or ?groups given by presentations in which each defining relator involves at most two ...
We extend previous results by Cumplido, Martin and Vaskou on parabolic subgroups of large-type Artin...
The class of groups defined by periodic paired relations, as introduced by Vinberg, includes the gen...
. The Tits conjecture claims that the subgroup generated by the squares of the standard generators o...
One says that the Tits alternative holds for a finitely generated group G if G contains either a non...
Artin groups, also called Artin-Tits groups, have been widely studied since their introduction by Ti...
We show the existence of several new infinite families of polynomially-growing automorphisms of free...
14 pagesA theorem of Cantat and Urech says that an analog of the classical Tits alternative holds fo...
We show that for every integer $d$, there is a constant $N(d)$ such that if $K$ is any field and $F$...
This paper is a short survey on four basic questions on Artin-Tits groups: the torsion, the center, ...
Tits proved that if G is a finitely generated linear group then G contains either a non abelian fre...
Rosenberger’s conjecture is proved for groups T(2,l,2,R) with l=6, 12, 30, 60 and some special group...
26 pages, 2 figuresLet $G=G_1\ast\dots\ast G_k\ast F$ be a countable group which splits as a free pr...
We conjecture that the word problem of Artin-Tits groups can be solved without introducing trivial f...