The title compound, C(15)H(12)N(2)OS, adopts a twisted V-shape, with the S atom as the pivot. The benzimidazole ring system [maximum deviation = 0.015 (1) Å] makes a dihedral angle of 78.56 (7)° with the phenyl ring. The O atom of the ketone group is close to coplanar with its adjacent ring [O-C-C-C torsion angle = 11.0 (2)°]. In the crystal, mol-ecules are linked by N-H⋯N hydrogen bonds into a...

There are two mol-ecules in the asymmetric unit of the title compound, C9H10N2OS. In one, the dihedral angle between the aromatic ring and the carbamo-thioyl group is 52.31 (7)° and in the other it is 36.16 (6)°. Each mol-ecule features an intra-molecular N-H⋯O hydrogen bond, which generates an S(6) ring and the O and S atoms have an anti disposition. In the crystal, mol-ecules are linked by N-...

Let X be the affine flag manifold of Lie type A1. Its moment graph encodes the torus fixed points (which are elements of the infinite dihedral group D∞) and the torus stable curves in X. Given a fixed point u ∈ D∞ and a degree d = (d0, d1) ∈ Z≥0, the combinatorial curve neighborhood is the set of maximal elements in the moment graph of X which can be reached from u using a chain of curves of to...

The adjacency spectrum Spec(Γ) of a graph Γ is the multiset of eigenvalues of its adjacency matrix. Two graphs with the same spectrum are called cospectral. A graph Γ is “determined by its spectrum” (DS for short) if every graph cospectral to it is in fact isomorphic to it. A group is DS if all of its Cayley graphs are DS. A group G is Cay-DS if every two cospectral Cayley graphs of G are isomo...

This research is about the group coverings of subsets finite non-abelian groups and its application in field cryptography. Group abelian has been researched over years it many applications various fields. The popularity internet increased rapidly cryptography become more important as ensures privacy security users network. A cryptosystem a structure consisting several cryptographic primitives. ...

in this paper we define s algebras and show that every finite group can be found in some s algebra.  we define and study the s degree of a finite group and determine the s degree of several classes of finite groups such as cyclic groups, elementary abelian $p$-groups, and dihedral groups $d_p$.