In the title compound, C(13)H(10)ClFO(3)S(2), the two-ring system is essentially planar, the mean plane of the benzene ring being inclined at 6.0 (2)° to the plane of the remaining four atoms. The ethyl-sulfanyl group is almost coplanar with the two rings [dihedral angle = 6.4 (2)°], while the carboxyl-ate group is almost perpendicular to it [dihedral angle = 72.4 (2)°]. In the crystal structur...

Let G be a group and S subset of such that e ∉ S−1 ⊆ S. Then Cay(G, S) is simple undirected Cayley graph whose vertices are all elements two x y adjacent if only xy−1 ∈ The size called the valency S). In this paper, we determined structure Cay(D2n, S), where D2n dihedral order 2n, n ≥ 3 |S| = 1, 2 or 3.

Quasi-cancellativity is the generalization of cancellativity. We introduce the notion of quasi-cancellativity of semigroup into AG-groupoids. We prove that every AG-band is quasi-cancellative. We also prove the famous Burmistrovich’s Theorem for AG-groupoids that states “An AG∗∗-groupoid S is a quasi-cancellative if and only if S is a semilattice of cancellative AG∗∗-groupoids”.

In the title compound, C(12)H(15)NO(6)S, the aromatic ring is oriented at dihedral angles of 64.76 (11) and 56.42 (13)° with respect to the planar methyl ester unit and the SO(2) group, respectively. The dihedral angle between the SO(2) group and the planar methoxy-carbonyl-methyl group is 50.42 (14)°. Intra-molecular C-H⋯O hydrogen bonding results in the formation of an eight-membered ring. In...

For Artin groups of dihedral type, we compute the Bredon homology classifying space for family virtually cyclic subgroups with coefficients in K-theory a group ring.

Let $D_4$ be the dihedral group of order $8$. In present study, we give generators algebra invariants in polynomial with four over a field characteristic zero.

In the title compound, C(11)H(14)N(2)O(5), the nitro group is approximately coplanar with the benzene ring, making a dihedral angle of 4.26 (17)°. The dihedral angle between the methyl-carbamate group and the benzene ring is 72.47 (6)°. There is a strong inter-molecular N-H⋯O hydrogen bond between the N and O atoms from adjacent methyl-carbamate groups, forming a one-dimensional network along t...

A 1978 theorem of Kozen states that two graphs on n vertices are isomorphic if and only if there is a clique of size n in the weak modular product between the two graphs. Restricting to bipartite graphs and considering complete bipartite subgraphs (bicliques) therein, we study the combinatorics of the weak modular product. We identify cases where isomorphism is tractable using this approach, wh...

In the title compound, C(17)H(17)NO(2), the phenyl-ene rings are bent with respect to the carbon-carbon double bond [dihedral angle between rings = 39.6 (1)°]. The acetamido group is twisted out of the plane of the aromatic ring [dihedral angle = 44.2 (1)°] in order to form an N-H⋯O hydrogen bond to the acetamido group of an adjacent mol-ecule, generating a zigzag chain running along the c axis.