Groups with infinite FC-center have the Schmidt property

A relation between infinite subsets and exterior center in groups

Let G be a group. Neumann to answer a question of Paul Erdos proved that every infinite subset of G has two different comuting elements  if and only if G is center-by-finite. In this paper, we deal with Erdoschr('39')s question in different aspect and we show that every infinite subset X of G has two different elements x and y such that x^y=1  if and only if the exterior  center of G ihas finit...

Divergence Groups Have the Bowen Property

Moore groups have the WS-property

Hilbert-schmidt Groups as Infinite-dimensional Lie Groups and Their Riemannian Geometry

We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for these groups. In particular, the Ricci curvature, which is understood as the limit of the Ricci curvature of finite-dimensional groups, is calculated. We show that for some of these groups the Ricci curvatu...

Pregarside Monoids and Groups, Parabolicity, Amalgamation, and FC Property

We define the notion of preGarside group slightly lightening the definition of Garside group so that all Artin-Tits groups are preGarside groups. This paper intends to give a first basic study on these groups. Firstly, we introduce the notion of parabolic subgroup, we prove that any preGarside group has a (partial) complemented presentation, and we characterize the parbolic subgroups in terms o...