1. Abstract characterization of Dn The group Dn has two generators r and s with orders n and 2 such that srs−1 = r−1. We will show any group with a pair of generators like r and s (except for their order) admits a homomorphism onto it from Dn, and is isomorphic to Dn if it has the same size as Dn. Theorem 1.1. Let G be generated by elements a and b where an = 1 for some n ≥ 3, b2 = 1, and bab−1...

Given a combinatorial description C of a polyhedron having E edges, the space of dihedral angles of all compact hyperbolic polyhedra that realize C is generally not a convex subset of R [9]. If C has five or more faces, Andreev’s Theorem states that the corresponding space of dihedral angles AC obtained by restricting to non-obtuse angles is a convex polytope. In this paper we explain why Andre...

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, $M(G,2)$.

in this paper we consider the group algebra $r(c_2times‎ ‎d_infty)$‎. ‎it is shown that $r(c_2times d_infty)$ can be‎ ‎represented by a $4times 4$ block circulant matrix‎. ‎it is also‎ ‎shown that $mathcal{u}(mathbb{z}_2(c_2times d_infty))$ is‎ ‎infinitely generated‎.

Abstract The space of Euclidean cone metrics on centrically symmetric octahedra with fixed angles ?i < 2 ? , total surface area 1, has a natural hyperbolic metric, and is locally isometric to 3-space. metric completion the ideal tetrahedron whose dihedral are half cone-deficits ? .

There are two crystallographically independent mol-ecules in the asymmetric unit of the title compound, C(22)H(17)BrN(6). The dihedral angles between the imidazo[4,5-b]pyridine mean plane and the phenyl rings are 20.4 (2) and 24.0 (2)° in the two mol-ecules. The orientation of triazoles compared to the imidazo[4,5-b]pyridine system is almost the same in both mol-ecules, with dihedral angles of ...

This paper deals with the classification of groups G such that power graphs and proper are line graphs. In fact, we classify all finite nilpotent whose Also, categorize (except non-abelian 2-groups) Moreover, investigate when generalized quaternion Besides, derive a condition on order dihedral for which