In the structure of the title compound (N26DCP2CBA), C(13)H(8)Cl(3)NO, the conformations of N-H and C=O bonds in the amide group are trans to each other, similar to that observed in N-(2,6-dichloro-phen-yl)benzamide, 2-chloro-N-phenyl-benzamide, 2-chloro-N-(2-chloro-phen-yl)benzamide and 2-chloro-N-(2,3-dichloro-phen-yl)benzamide with similar bond parameters. Furthermore, the position of the am...

We construct the Darboux transformation with Dihedral reduction group for the 2–dimensional generalisation of the periodic Volterra lattice. The resulting Bäcklund transformation can be viewed as a nonevolutionary integrable differential difference equation. We also find its generalised symmetry and the Lax representation for this symmetry. Using formal diagonalisation of the Darboux matrix we ...

The title compound, C(15)H(12)ClNO, a substituted chalcone, adopts an E configuration with respect to the C=C bond of the enone unit. The mol-ecule is not planar, as can be seen from the dihedral angle of 28.9 (2)° between the two rings which are twisted from each other. The enone segment of the mol-ecule is not coplanar with the chloro-phenyl ring, making a dihedral angle of 23.4 (3)° with it....

In 1976, B. H. Neumann [4] characterized the central-by-finite groups by the following property: the group G is central-by-finite if and only if it does not contain an infinite independent subset, where a subset U of G is called independent if uv = vu for u,veUimplies u = v. More recently, P. Longobardi, M. Maj and the first author [2] considered a more general class of groups, the deficient sq...

‎in this paper‎, ‎we obtain the dimensions of symmetry classes of polynomials associated with‎ ‎the irreducible characters of the dihedral group as a subgroup of‎ ‎the full symmetric group‎. ‎then we discuss the existence of o-basis‎ ‎of these classes‎.

In this paper, we compute the number of fuzzy subgroups of some classes of non-abeilan groups. Explicit formulas are givenfor dihedral groups $D_{2n}$, quasi-dihedral groups $QD_{2^n}$, generalized quaternion groups $Q_{4n}$ and modular $p$-groups $M_{p^n}$.