There exist infinite, finitely presented, torsion-free groups G such that Aut(G) and Out(G) are torsion-free but G has an automorphism sending some non-trivial element to its inverse.

In this article, we formalize a torsion Z-module and a torsionfree Z-module. Especially, we prove formally that finitely generated torsion-free Z-modules are finite rank free. We also formalize properties related to rank of finite rank free Z-modules. The notion of Z-module is necessary for solving lattice problems, LLL (Lenstra, Lenstra, and Lovász) base reduction algorithm [20], cryptographic...

We prove that the generic type of a non-cyclic torsion-free hyperbolic group G is foreign to any interpretable abelian group, hence also to any interpretable field. This result depends, among other things, on the definable simplicity of a non-cyclic torsion-free hyperbolic group, and we take the opportunity to give a proof of the latter using Sela’s description of imaginaries in torsion-free hy...

The structural and energetic determinants for kinking a basepair step by minor groove-insertion of the protein side chains of PurR, LacI, LEF-1, IHF, Sac7d, and Sso7d, have been calculated by molecular dynamics/potential of mean force simulations. The structural determinants of the kinked structures are: two contiguous furanose rings achieve different conformations, in the region of C3'endo (A-...

A language is torsion (resp. bounded torsion, aperiodic, bounded aperiodic) if its syntactic monoid is torsion (resp. bounded torsion, aperiodic, bounded aperiodic). We generalize the regular language theorems of Kleene, Sch utzenberger and Straubing to describe the classes of torsion, bounded torsion, aperiodic and bounded aperiodic languages. These descriptions involve taking limits of sequen...

We provide a solution to the isomorphism problem for torsion-free relatively hyperbolic groups with abelian parabolics. As special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished); and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]). We also give a solution to the homeomorp...

The introduction of a covariant derivative on the velocity phase space is needed for a global expression of Euler-Lagrange equations. The aim of this paper is to show how its torsion tensor turns out to be involved in such a version. Submitted to: J. Phys. A: Math. Gen. PACS numbers: 45.10.Na 02.40.Yy The introduction of numbers as coordinates. . . is an act of violence Hermann Weyl An increasi...

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...

Problem statement: Algebraic K-theory of projective modules over commutative rings were introduced by Bass and central simple superalgebras, supercommutative super-rings were introduced by many researchers such as Knus, Racine and Zelmanov. In this research, we classified the projective supermodules over (torsion free) supercommutative super-rings and through out this study we forced our selves...

The isomorphism problem for group algebras over a field with arbitrary characteristic of some special classes of torsion-free non-abelian groups is explored. Specifically, the following are proved: Suppose F is a field and G is a torsion-free group with centre C(G) such that FG ∼= FH as F -algebras for any group H . Then it is shown that H is torsion-free (provided that FG is without zero divis...