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...

The dimension of any module over an algebra of affiliated operators U of a finite von Neumann algebra A is defined using a trace on A. All zero-dimensional U-modules constitute the torsion class of torsion theory (T,P). We show that every finitely generated U-module splits as the direct sum of torsion and torsion-free part. Moreover, we prove that the theory (T, P) coincides with the theory of ...

We review the notion of Gieseker stability for torsion-free Higgs sheaves. This notion is a natural generalization of the classical notion of Gieseker stability for torsion-free coherent sheaves. We prove some basic properties that are similar to the classical ones for torsion-free coherent sheaves over projective algebraic manifolds. In particular, we show that Gieseker stability for torsion-f...

In this paper we seek to describe the structure of self-dual torsion-free LCA groups. We first present a proof of the structure theorem of self-dual torsion-free metric LCA groups. Then we generalize the structure theorem to a larger class of selfdual torsion-free LCA groups. We also give a characterization of torsion-free divisible LCA groups. Consequently, a complete classification of self-du...

In this paper the cotypeset of some torsion-free abelian groups of finite rank is studied. In particular, we determine the cotypeset of some rank two groups using the elements of their typesets. Introduction One of the important and known tools in the theory of torsion-free abelian groups is type and the typeset of a group. This set which is determined from the beginning of the the study the to...