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 ...

We construct a new infinite family of four-dimensional isolated symplectic singularities with trivial local fundamental group, answering question Beauville raised in 2000. Three constructions are presented for this family: (1) as blowups the quotient C 4 $\mathbb {C}^4$ by dihedral group order 2 d $2d$ , (2) singular points Calogero–Moser spaces associated groups at equal parameters, and (3) ce...

In the title compound, C(16)H(12)BrFO(2), the dihedral angle between the aromatic rings is 23.75 (12)° and the dihedral angle between the prop-2-en-1-one fragment and the fluorobenzene ring is 20.9 (2)°. In the crystal, only van der Waals interactions occur.

Since the first years of structural biology, Ramachandran map has provided a simple definition curvilinear geometry protein backbone. Its is mainly based on values dihedral angles $$\phi $$ and $$\psi measured between heavy atoms Discontinuities in angle are observed, particularly region $$\beta -strand secondary structure. We introduce new pseudo-dihedral involving hydrogen positions instead s...

In the title mol-ecule, C(22)H(18)N(2)O(5), the nitro-substituted ring makes a dihedral angle of 81.9 (1)° with the benzoyl ring and a dihedral angle of 12.1 (1)° with the methyl-substituted ring.

Recently, several works by a number of authors have provided characterizations integral undirected Cayley graphs over generalized dihedral groups and dicyclic groups. We generalize unify these results in two different ways. Firstly, we work arbitrary non-abelian finite admitting an abelian subgroup index 2. Secondly, our main result actually characterizes mixed such groups, the spirit very rece...

In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.

In the title compound, C(23)H(22)N(2)O(2), the central pyrazole ring is nearly planar (r.m.s. deviation = 0.046 Å) and it makes a dihedral angle of 18.5 (2)° with the phenyl ring. The dihedral angles between the phenyl and the two meth-oxy-substituted phenyl rings are 26.2 (2) and 80.6 (2)°. The crystal structure is stabilized by C-H⋯π stacking inter-actions and weak π-π inter-actions [centriod...

The asymmetric unit of the title compound, C(20)H(18)O(8), contains two mol-ecules with small geometric differences. The dihedral angles between the benzene rings are 62.94 (12) and 59.99 (12)°. The dihedral angles between the carboxylate groups in the 2- and 3-positions are 81.72 (13) and 65.54 (15)°, respectively. However, the dihedral angles between the carboxylate groups in the 3' and 4'-po...

in this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.