Regular neighbourhoods and canonical decompositions for groups.
Relation modules of finite groups and related topics.
Relation modules of infinite groups, II
Let F n denote the free group of rank n and d(G) the minimal number of generators of the finitely generated group G. Suppose that R ↪ F m ↠ G and S ↪ F m ↠ G are presentations of G and let and denote the associated relation modules of G. It is well known that even though it is quite possible that . However, to the best of the author’s knowledge no examples have appeared in the literature with the property that . Our purpose here is to exhibit, for each integer k ≥ 1, a group G that has presentations...
Relations among the squares of the generators of the braid groups.
Relative commutator associated with varieties of -nilpotent and of -solvable groups
In this note we determine explicit formulas for the relative commutator of groups with respect to the subvarieties of -nilpotent groups and of -solvable groups. In particular these formulas give a characterization of the extensions of groups that are central relatively to these subvarieties.
Relative property (T) and linear groups
Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following result: A finitely generated group admits a special linear representation with non-amenable -Zariski closure if and only if it acts on an Abelian group (of...
Remarks on Characters of Discrete Nilpotent Groups.
Remarks on free Bieberbach Groups.
Remarks on the Mal'cev completion of torsion-free locally nilpotent groups
Representation of Markoff's binary quadratic forms by geodesics on a perforated torus
Representation of order automorphisms by words.
Représentations de certains groupes symplectiques finis
Représentations de dimension finie de l’algèbre de Cherednik rationnelle
On donne une condition nécessaire et suffisante pour l’existence de modules de dimension finie sur l’algèbre de Cherednik rationnelle associée à un système de racines.
Representations linearies et compactification profinie des groupes discrets.
Representations of (1,1)-knots
We present two different representations of (1,1)-knots and study some connections between them. The first representation is algebraic: every (1,1)-knot is represented by an element of the pure mapping class group of the twice punctured torus PMCG₂(T). Moreover, there is a surjective map from the kernel of the natural homomorphism Ω:PMCG₂(T) → MCG(T) ≅ SL(2,ℤ), which is a free group of rank two, to the class of all (1,1)-knots in a fixed lens space. The second representation is parametric: every...
Representations of a free group of rank two by time-varying Mealy automata
In the group theory various representations of free groups are used. A representation of a free group of rank two by the so-calledtime-varying Mealy automata over the changing alphabet is given. Two different constructions of such automata are presented.
Representations of Certain Verbal Wreath Products by Matrices.
Representations of Coxeter Groups and Hecke Algebras.
Representations of cyclically ordered groups
Representations of polygons of finite groups.