In the title compound, C(16)H(16)BrNO(4), the dihedral between the planes of the aromatic rings is 7.74 (18)°. The amide group is tilted with respect to the bromo- and meth-oxy-substituted aromatic rings by 36.3 (8) and 35.2 (8)°, respectively. The meta-meth-oxy groups are essentially in-plane with the aromatic ring [dihedral angles CH(3)-O-C-C = -4.6 (4) and -2.5 (4)°]. The para-meth-oxy group...

Let $C_n$, $Q_n$ and $D_n$ be the cyclic group, quaternion group dihedral of order $n$, respectively. Recently, structures unit groups finite algebras $2$-groups that contain a normal subgroup index $2$ have been studied. The $D_{2n}, n\geq 3$ generalized $Q_{4n}, 2$ also $2$. $FQ_{12}$, $FD_{12}$, $F(C_2 \times Q_{12})$ D_{12})$ over field $F$ are well known. In this article, we continue inves...

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 ...

Abstract Let G be a p -group for some prime . Recall that the Hughes subgroup of is generated by all elements with order not equal to In this paper, we prove if cyclic, then has exponent or cyclic dihedral. We also generalised quaternion, must quaternion. With these results in hand, classify tidy -groups.

We show that most of the genus-zero subgroups braid group $\mathbb{B}_3$ (which are roughly monodromy groups trigonal curves on Hirzebruch surfaces) irrelevant as far Alexander invariant is concerned: there a very restricted class \enquote{primitive} such these and their intersections determine all invariants. Then, we classify primitive in special subclass. This result implies known classifica...

We study the trigonometry of non-Euclidean tetrahedra using tools from algebraic geometry. establish a bijection between and certain rational elliptic surfaces. interpret edge lengths dihedral angles tetrahedron as values period maps for corresponding surface. As corollary we show that cross-ratio exponents solid is equal to perimeters its faces. The Regge symmetries are related action Weyl gro...

For a given element $g$ of finite group $G$, the probablility that commutator randomly choosen pair elements in $G$ equals is relative commutativity degree $g$. In this paper we are interested studying Dihedral order $2n$ and Quaternion $2^{n}$ for any $n\geq 3$ examine infinite class Moufang Loops Chein type, $M(G,2)$.