Finitely Generated Metabelian Groups are not Subnormality Separable.
Finitely Generated pro-2 Groups with a free subgroup of Index 2.
Finitely generated soluble groups with an Engel condition on infinite subsets
Finiteness of a non-abelian tensor product of groups.
Finiteness Properties of Duality Groups
Finiteness Theorems for Deformations of Complexes
We consider deformations of bounded complexes of modules for a profinite group over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex to be represented by a complex of -modules that is strictly perfect over the associated versal deformation ring.
First-order definability and algebraicity of the sets of annihilating and generating collections of elements for some relatively free solvable groups.
Fixed points for positive permutation braids
Making use of the Nielsen fixed point theory, we study a conjugacy invariant of braids, which we call the level index function. We present a simple algorithm for computing it for positive permutation cyclic braids.
Fixed points of endomorphisms of certain free products
The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.
Fixed points of endomorphisms of certain free products
The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.
Foldable cubical complexes of nonpositive curvature.
Folner sets of alternate directed groups
An explicit family of Folner sets is constructed for some directed groups acting on a rooted tree of sublogarithmic valency by alternate permutations. In the case of bounded valency, these groups were known to be amenable by probabilistic methods. The present construction provides a new and independent proof of amenability, using neither random walks, nor word length.
For Coxeter groups is a coefficient of a uniformly bounded representation
We prove the theorem in the title by constructing an action of a Coxeter group on a product of trees.
Formally Real Fields with a Simple Description of the Absolute Galois Group.
Fractal representation of the attractive lamination of an automorphism of the free group
In this paper, we extend to automorphisms of free groups some results and constructions that classically hold for morphisms of the free monoid, i.e., the so-called substitutions. A geometric representation of the attractive lamination of a class of automorphisms of the free group (irreducible with irreducible powers (iwip) automorphisms) is given in the case where the dilation coefficient of the automorphism is a unit Pisot number. The shift map associated with the attractive symbolic lamination...
Frattini Covers and Projective Groups Without the Extension Property.
Frattini normal subgroups of finite groups.
Frattini-eingebettete Normalteiler. II.
Free and non-free subgroups of the fundamental group of the Hawaiian Earrings
The space which is composed by embedding countably many circles in such a way into the plane that their radii are given by a null-sequence and that they all have a common tangent point is called “The Hawaiian Earrings”. The fundamental group of this space is known to be a subgroup of the inverse limit of the finitely generated free groups, and it is known to be not free. Within the recent move of trying to get hands on the algebraic invariants of non-tame (e.g. non-triangulable) spaces this space...
Free group languages : rational versus recognizable
We provide alternative proofs and algorithms for results proved by Sénizergues on rational and recognizable free group languages. We consider two different approaches to the basic problem of deciding recognizability for rational free group languages following two fully independent paths: the symmetrification method (using techniques inspired by the study of inverse automata and inverse monoids) and the right stabilizer method (a general approach generalizable to other classes of groups). Several...