In this paper we complete the characterization of Ext(G, Z) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence of cardinals (νp : p ∈ Π) satisfying νp ≤ 2 , ...

Let R be any ring (with 1), G a torsion free group and RG the corresponding group ring. Let Ext∗RG(M,M) be the cohomology ring associated to the RG-module M . Let H be a subgroup of finite index of G. The following is a special version of our main Theorem: Assume the profinite completion of G is torsion free. Then an element ζ ∈ Ext∗RG(M,M) is nilpotent (under Yoneda’s product) if and only if i...

Sufficient conditions are given for groups of finite Morley rank having non-trivial torsion-free nilpotent normal subgroups to have linear representations with small kernels. In particular, centreless connected soluble groups of finite Morley rank with torsion-free Fitting subgroups have faithful linear representations. On the way, using a notion of definable weight space, we prove that certain...

Background & aim: Ovarian torsion is one of the most common causes of emergency surgery in gynecology, with a tendency to occur in postmenopausal women. The aim of this study was to provide information concerning the clinical presentations, surgical management, pathological findings and risk of malignancy in postmenopausal women with ovarian torsion. Methods:In this cross-sectional study, the r...

In this paper, we discuss a relation between Jones-Witten theory of knot invariants and topological open string theory on the basis of the volume conjecture. We find a similar Hamiltonian structure for both theories, and interpret the AJ conjecture as the D-module structure for a D-brane partition function. In order to verify our claim, we compute the free energy for the annulus contributions i...

This paper is a short survey on four basic questions on Artin-Tits groups: the torsion, the center, the word problem, and the cohomology (K(π, 1) problem). It is also an opportunity to prove three new results concerning these questions: (1) if all free of infinity Artin-Tits groups are torsion free, then all Artin-Tits groups will be torsion free; (2) If all free of infinity irreducible non-sph...