The asymmetric unit of the title compound, (C(8)H(11)N(2)S)(2)[ZnCl(4)], contains two S-benzyl-isothio-uronium cations which differ in the C-C-S-C torsion angle [165.3 (2) and 81.9 (2)°] and a tetrahedral tetra-chloridozincate anion. The crystal structure is stabilized by N-H⋯Cl, C-H⋯Cl and C-H⋯S inter-actions.

The title compound, C(25)H(34)N(2)O(3)S, is a derivative of N'-benzyl-ideneacetohydrazide having substituents on the acetyl and benzylidenyl parts, and displays a planar C(carbon-yl)-NH-NC(anis-yl) fragment [torsion angle = 174.9 (3)°]. The -NH- unit forms an N-H⋯O hydrogen bond with the carbonyl O atom of an inversion-related mol-ecule.

The unit conjecture, commonly attributed to Kaplansky, predicts that if $K$ is a field and $G$ torsion-free group, then the only units of group ring $K[G]$ are trivial units, is, non-zero scalar multiples elements. We give concrete counterexample this conjecture; virtually abelian order two.

We investigate the possible character values of torsion units of the normalized unit group of the integral group ring of Mathieu sporadic groupM22. We confirm the Kimmerle conjecture on prime graphs for this group andspecify the partial augmentations for possible counterexamples to the stronger Zassenhaus conjecture.

In the title compound, C(11)H(15)N(3)O(3), one of the methyl groups attached to the benzamide unit is slightly twisted with a C-N-C-C torsion angle of 4.04 (13)°. The crystal packing is stabilized by weak intermolecular C-H⋯O hydrogen bonds together with a weak C-H⋯π inter-action.

In this paper, we find the unit tangent vector and the geodesic torsion of the tangential intersection curve of two surfaces in all three types of surface-surface intersection problems (parametric-parametric, implicit-implicit and parametric-implicit) in three-dimensional Euclidean space.

The title compound, C(28)H(21)N(3)S, crystallizes with two mol-ecules in the asymmetric unit. There are only very slight differences in the torsion angles between the two molecules. The two mol-ecules are stabilized by intra-molecular N-H⋯N inter-actions and the crystal packing is stabilized by inter-molecular N-H⋯S inter-actions.

The title compound, C17H29NO4, contains a chiral center and crystallizes as a racemate. The asymmetric unit consists of two non-equivalent mol-ecules, in which the carbeth-oxy groups have markedly different orientations [C(=O)CC(OEt)=O torsion angles = 59.3 (2) and 156.0 (2)°]. In the crystal, mol-ecules form chains along [101] through N-H⋯O hydrogen bonds.

Given a λ-regular SU(2) or SL(2,C)-representation of a knot group, we show how to calculate non-abelian twisted Reidemeister torsion of its knot exterior. This method is due to considering the relationship between a zero of acyclic Reidemeister torsion and non-acyclic Reidemeister torsion. We calculate some examples and investigate the behavior of non-abelian SU(2)-twisted Reidemeister torsion ...

Given a λ-regular SU(2) or SL(2,C)-representation of a knot group, we show a relationship between a zero of acyclic Reidemeister torsion and non-acyclic Reidemeister torsion. Then we can give a method to calculate non-abelian twisted Reidemeister torsion of its knot exterior. We calculate some examples and investigate the behavior of non-abelian SU(2)-twisted Reidemeister torsion associated to ...