https://sciold.ui.ac.ir/~a.abdollahi/PDF/comm-graph.pdf

Non-commuting graph of a group ✩

On monomial algebras

Nous developpons des methodes dynamiques pour etudier les groupes ordonnables ainsi que leurs espaces d'ordres associes. Nous donnons des preuves nouvelles et elementaires de theoremes dus a Linnell (si un groupe ordonnable possede une infinite d'ordres, alors il en possede une infinite non denombrable) et McCleary (l'espace des ordres du groupe libre est un ensemble de Cantor). Nous montrons que ce dernier resultat est valable aussi pour les groupes nilpotents denombrables et sans torsion qui ne sont pas abeliens de rang un. Finalement, nous appliquons nos methodes au cas des groupes de tresses. En particulier, nous demontrons que le cone positif de l'ordre de Dehornoy n'est pas de type fini en tant que semi-groupe. Pour ce faire, nous definissons le noyau conradien d'un ordre comme etant le plus grand sous-groupe convexe sur lequel la relation est conradienne, et nous travaillons avec cette notion.

/pdf/on-the-dynamics-of-left-orderable-groups-59iax93rvg.pdf

On the dynamics of (left) orderable groups

Structure of a group and the structure of its lattice of subgroups

Let Γ be a finitely generated, amenable group. Using an idea of E Ghys, we prove that if Γ has a nontrivial, orientation-preserving action on the real line, then Γ has an infinite, cyclic quotient. (The converse is obvious.) This implies that if Γ has a faithful action on the circle, then some finite-index subgroup of Γ has the property that all of its nontrivial, finitely generated subgroups have infinite, cyclic quotients. It also means that every left-orderable, amenable group is locally indicable. This answers a question of P Linnell.

/pdf/amenable-groups-that-act-on-the-line-20strr551c.pdf

Amenable groups that act on the line

A permutational property of groups

Two new criteria for solvability of finite groups

An exact upper bound for sums of element orders in non-cyclic finite groups

/pdf/a-note-on-locally-graded-groups-wshpjcutmo.pdf

A note on locally graded groups

We look at groups which have no (nonabelian) free subsemigroups. It is known that a finitely generated solvable group with no free subsemigroup is nilpotent-by-finite. Conversely nilpotent-by-finite groups have no free subsemigroups. Torsion-free residually finitep groups with no free subsemigroups can have very complicated structure, but with some extra condition on the subsemigroups of such a group one obtains satisfactory results. These results are applied to ordered groups, right-ordered groups, and locally indicable groups.

/pdf/groups-with-no-free-subsemigroups-3sfg5ii7s7.pdf

Patrizia Longobardi

Papers

A permutational property of groups

Two new criteria for solvability of finite groups

An exact upper bound for sums of element orders in non-cyclic finite groups

A note on locally graded groups

Groups with no free subsemigroups