‎In the classical group theory there is‎ an open question‎: ‎Is every torsion free n-Engel group (for n ≥ 4)‎, nilpotent?‎. ‎To answer the question‎, ‎Traustason‎ [11] showed that with some additional conditions all‎ ‎4-Engel groups are locally nilpotent‎. ‎Here‎, ‎we gave some partial‎ answer to this question on Engel fuzzy subgroups‎. ‎We show that if μ is a normal 4-Engel fuzzy‎ subgroup of ...

The methods of effective field theory are used to explore the theoretical and phenomenological aspects of the torsion field. Spinor action coupled to electromagnetic field and torsion possesses an additional softly broken gauge symmetry. This symmetry enables one to derive the unique form of the torsion action compatible with unitarity and renormalizability. It turns out that the antisymmetric ...

In this paper we make two observations related to discrete torsion. First, we observe that an old obscure degree of freedom (momentum/translation shifts) in (symmetric) string orbifolds is related to discrete torsion. We point out how our previous derivation of discrete torsion from orbifold group actions on B fields includes these momentum lattice shift phases, and discuss how they are realize...

In this work we present the general differential geometry of a background in which space-time has both torsion and curvature with internal symmetries being described by gauge fields, that is equipped to couple spinorial matter fields having spin energy as well currents: will turn out be equivalent an axial-vector massive Proca field because spinor can decomposed its two chiral projections, thou...

Let R be an hereditary Noetherian prime ring, let S be a "Dedekind closure" of R and let T be the category of finitely generated S-torsion R-modules. It is shown that for all i ~ 0, there is an exact sequence 0 -> Ki(T) -> Ki(R) -> Ki(S) ...... O. If i = 0, or R has finitely many idempotent ideals then this sequence splits. A notion of ''right ideal class group" is then introduced for hereditar...

We show that the universal theory of torsion groups is strongly contained in the universal theory of finite groups. This answers a question of Dyson. We also prove that the universal theory of some natural classes of torsion groups is undecidable. Finally we observe that the universal theory of the class of hyperbolic groups is undecidable and use this observation to construct a lacunary hyperb...

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for Evans’ theory and show that it yields two field equations. The second field equation is algebraic in the torsion...

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...