In the crystal of the title compound, C11H14O4, the aromatic ring is almost coplanar with the 2-position meth-oxy group with which it subtends a dihedral of 0.54 (2)°, while the 5-position meth-oxy group makes a corresponding dihedral angle of just 5.30 (2)°. The angle between the mean planes of the aromatic ring and the propionic acid group is 78.56 (2)°. The fully extended propionic side chai...

In the title compound, C(23)H(26)N(2)O(2)S, the sulfur-bound phenyl group is aligned approximately parallel to one of the two rings of the benzhydryl group, making a dihedral angle of 1.15 (9)°. The other forms a dihedral angle of 59.20 (9)° with the phenyl group bound to the S atom. In the crystal, mol-ecules are linked into strands along [100] by weak C-H⋯O contacts. Weak C-H⋯π inter-actions ...

In the racemic title compound, C(14)H(17)NO(6), the plane of the ester group of the methyl hexa-noate side chain makes a dihedral angle of 80.0 (2)° with the benzene ring, while the nitro group is approximately coplanar with the benzene ring [dihedral angle = 10.3 (2)°]. In the crystal, mol-ecules form weak aromatic C-H⋯O(nitro) hydrogen-bonding inter-actions, giving inversion dimers [graph set...

Recently, a new parameter of a code, referred to as the remoteness, has been introduced.This parameter can be viewed as a dual to the covering radius. It is exactly determined for the cyclic and dihedral groups. In this paper, we consider the group $U_{6n}$ as a subgroup of $S_{2n+3}$ and obtain its remoteness.  We show that the remoteness of the permutation code $U_{6n}$ is $2n+2$.  Moreover, ...

IT is well known that every group which contains at least one operator of order 2 must contain an odd number of such operators and that there is an infinite number of groups such that each of them contains exactly 2m + 1 operators of order 2, where m is an arbitrary positive integer or 0. It is also known that if exactly one half of the operators of a group are of order 2 then the order of this...

A group is called morphic if for each normal endomorphism α in end(G),there exists β such that ker(α)= Gβ and Gα= ker(β). In this paper, we consider the case that there exist normal endomorphisms β and γ such that ker(α)= Gβ and Gα = ker(γ). We call G quasi-morphic, if this happens for any normal endomorphism α in end(G). We get the following results: G is quasi-morphic if and only if, for any ...

The method of constructing the generalized dihedral group as a semidirect product an abelian and Z2 integers modulo 2 is extended to case gyrogroups. This leads study new class gyrogroups, which includes groups special case. In this article, we show that any dihedralizable gyrogroup can be enlarged dihedralized gyrogroup. Then, establish algebraic properties gyrogroups well combinatorial their ...