On some center-like subsets of groups.
The aim for the present paper is to study the theory of P-localization of a group in a category C such that it contains the category of the nilpotent groups as a full sub-category. In the second section we present a number of results on P-localization of a group G, which is the semi-direct product of an abelian group A with a group X, in the category G of all groups. It turns out that the P-localized (GP) is completely described by the P-localized XP of X, A and the action w of X on A. In the third...
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...