Search
Search Results
-
Linear Representations of the Automorphism Group of a Free Group
Let F n be the free group on n ≥ 2 elements and Aut( F n ) its group of automorphisms. In this paper we present a rich collection of linear...
-
Hall’s Theorem for Limit Groups
A celebrated theorem of Marshall Hall Jr. implies that finitely generated free groups are subgroup separable and that all of their finitely generated...
-
(Cyclic) subgroup separability of HNN and split extensions
This work has been divided in two parts. In the first part we give a sufficient conditions on an HNN extension of a free group to be cyclic subgroup...
-
On a free group of transformations defined by an automaton
We prove that three automorphisms of the rooted binary tree defined by a certain 3-state automaton generate a free non-Abelian group of rank 3.
-
Diophantine geometry over groups VI: the elementary theory of a free group
This paper is the sixth in a sequence on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and...
-
On hyperbolic once-punctured-torus bundles II: fractal tessellations of the plane
We describe fractal tessellations of the complex plane that arise naturally from Cannon–Thurston maps associated to complete, hyperbolic,...
-
Sturmian morphisms, the braid group B 4, Christoffel words and bases of F 2
We give a presentation by generators and relations of a certain monoid generating a subgroup of index two in the group Aut( F 2 ) of automorphisms of...
-
Anti-tori in Square Complex Groups
An anti-torus is a subgroup 〈 a , b 〉 in the fundamental group of a compact non-positively curved space X , acting in a specific way on the universal...
-
Free groups and involutions in the unit group of a group algebra
We study the existence of free groups of rank 2 in the group generated by the involutions in the unit group of a group algebra over a non-absolute...
-
Diophantine geometry over groups V2: quantifier elimination II
This paper is the sixth in a sequence on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and...
-
Parafree Groups
A group is termed parafree if it is residually nilpotent and has the same nilpotent quotients as a given free group. The object of this paper is, in...
-
The Finitary Andrews-Curtis Conjecture
The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected...
-
Algebraic Map**-Class Groups of Orientable Surfaces with Boundaries
Let Sg,b,p denote a surface which is connected, orientable, has genus g, has b boundary components, and has p punctures. Let Σg,b,p denote the...
-
Subgroups of Free Groups: a Contribution to the Hanna Neumann Conjecture
We prove that the strengthened Hanna Neumann conjecture, on the rank of the inter-section of finitely generated subgroups of a free group, holds for...
-
Counting Primitive Elements in Free Groups
In this paper it is proved that the set of primitive elements of a non-Abelian free group has density zero, i.e. the ratio of primitive elements in...
-
On Hyperbolic Once-Punctured-Torus Bundles
For a hyperbolic once-punctured-torus bundle over a circle, a choice of normalization determines a family of arcs in the Riemann sphere. We show...
-
The residual finiteness of negatively curved polygons of finite groups
A subgroup M ⊂ G is almost malnormal provided that for each g ∈ G − M , the intersection M g ∩ M is finite. It is proven that the free product of two...