Vanishing of the first-order cohomology on Olshanski spherical pairs

In this paper, we study the first-order cohomology space of countable direct limit groups related to Olshanski spherical pairs, relatively to unitary representations which do not have almost invariant vectors. In particular, we prove a variant of Delorme’s vanishing result of the first-order cohomology space for spherical representations of Olshanski spherical pairs.

Detecting conjugacy stability of subgroups in certain classes of groups

In this paper, we consider the conjugacy stability property of subgroups and provide effective procedures to solve the problem in several classes of groups. In particular, we start with free groups, that is, we give an effective procedure to find out if a finitely generated subgroup of a free group is conjugacy stable. Then we further generalize this result to quasi-convex subgroups of torsion-free hyperbolic groups and finitely generated subgroups of limit groups.

Non-∀-homogeneity in free groups

We prove that non-abelian free groups of finite rank at least 3 or of countable rank are not [Formula: see text]-homogeneous. We answer three open questions from Kharlampovich, Myasnikov, and Sklinos regarding whether free groups, finitely generated elementary free groups, and non-abelian limit groups form special kinds of Fraïssé classes in which embeddings must preserve [Formula: see text]-formulas. We also provide interesting examples of countable non-finitely generated elementary free groups.

Effective construction of covers of canonical Hom-diagrams for equations over torsion-free hyperbolic groups

We show that, given a finitely generated group G as the coordinate group of a finite system of equations over a torsion-free hyperbolic group Γ, there is an algorithm which constructs a cover of a canonical solution diagram. The diagram encodes all homomorphisms from G to Γ as compositions of factorizations through Γ-NTQ groups and canonical automorphisms of the corresponding NTQ-subgroups. We also give another characterization of Γ-limit groups as iterated generalized doubles over Γ.

JSJ DECOMPOSITIONS OF DOUBLES OF FREE GROUPS

We classify all possible JSJ decompositions of doubles of free groups of rank two, and we also compute the Makanin–Razborov diagram of a particular double of a free group and deduce that in general limit groups are not freely subgroup separable.

Ceny leków – teoria i praktyka

Drug prices – theory and practice Prices of reimbursed drugs in Poland are regulated by law and closely monitored, which has been specified in reimbursement act. It contains, among others, rules regarding drug pricing, payments, limit groups and it also defines mechanisms of access to reimbursed medicines. In addition to aforementioned reimbursement act, the important role in drug policy in Poland plays the Economic Commission operating at the Ministry of Health and the European Commission. Current rules of drug financing from public funds in Poland are precisely detailed, and therefore may be incomprehensible to a large part of society. The aim of this publication is to present theoretical aspects of drug reimbursement and associated with this most common problems in practice.