There are two independent mol-ecules (A and B) in the asymmetric unit of the title compound C11H10BrClO2, which represents the Z isomer. The methyl-acrylate moieties are essentially planar, within 0.084 (2) and 0.027 (5) Å in mol-ecules A and B, respectively. The benzene ring makes dihedral angles of 13.17 (7) and 27.89 (9)° with the methyl-acrylate moiety in mol-ecules A and B, respectively. T...

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(30)H(20)N(2)O(2), the orientation of the furyl group may induce a variety of coordination modes with this ligand. The dihedral angle between the two naphthyl rings is 79.25 (7)°. The furyl groups make dihedral angles of 62.0 (1) and 16.3 (2)° with the attached naphthyl groups. The dihedral angle between the two furyl rings is 49.3 (2)°.

In the title compound, C17H16O4, the dihedral angle between the benzene rings is 21.22 (1)° and the mean plane of the prop-2-en-1-one group makes dihedral angles of 10.60 (1) and 11.28 (1)°, respectively, with those of the hy-droxy-phenyl and eth-oxy-phenyl rings. The eth-oxy substituent forms a dihedral angle of 88.79 (2)° with the the prop-2-en-1-one group, which is found to be slightly twist...

In the title compound, C(21)H(30)N(2)O(5)S, the plane of the dimeth-yl-thio-carbamic group makes a dihedral angle of 78.41 (7)° with the central benzene ring. One of the carbonyl groups in the α,β-unsaturated malonate side chain makes a dihedral angle of 8.73 (10)° with the central benzene ring, while the other carbonyl group makes a dihedral angle of 81.52 (8)°.

Let G = Cm p o C2 be a generalized dihedral group for an odd prime and natural number m, L M(G; 2) the RA2 loop obtained from F finite field of characteristic 2. For algebra F[L], we determine Jacobson radical J(F[L]) F[L] Wedderburn decomposition F[L]=J(F[L]). The structure 1 + is also determined.