We give a new framework for the construction of homogeneous nilpotent groups and rings which goes a long way toward unifying the two cases, and enables us to extend previous constructions, producing a variety of new examples. In particular we find ingredients for the manufacture of 2No homogeneous nilpotent groups "in nature".

Molecular geometry, electronic spectra, infrared and NMR spectra of [Ru(OAc)(2mqn)2NO] (H2mqn = 2methyl-8-quinolinol) isomers were studied with density functional theory (DFT) at B3LYP level with 6311++G(d,p) and Aug-cc-pVDZ-PP as basis set. a r t i c l e i n f o

In the title compound, C(11)H(15)N(3) (2+)·2NO(3) (-), one of the imidazole N atoms and the N atom of the pyrrolidine ring are protonated. The pyrrolidine ring adopts an envelope conformation, with the C atom carrying the benzoimidazolium substituent as the flap atom. In the crystal structure, cations and anions are linked through N-H⋯O hydrogen bonds, forming chains that run parallel to the c ...

The crystal structure of the title compound, C(10)H(26)N(2) (2+)·2NO(3) (-), exhibits a back-to-back paired double-stacked packing arrangement culminating in an overall double zigzag pattern of the dications. Each pair of double-stacked dications is surrounded by a ring of ten nitrate anions. An intricate three-dimensional N---H...O and N---H...(O,O) hydrogen-bonding network exists in the cryst...

The title compound, C(12)H(18)N(8) (2+)·2NO(3) (-)·2H(2)O, was synthesized unexpectedly from 3-amino-1-methyl-1,4,5,6-tetra-hydro-pyrrolo-[3,4-c]pyrazol-5-ium chloride and cerium(IV) ammonium nitrate. The cation has a crystallographically imposed centre of symmetry. In the crystal, the ions and water mol-ecules are linked via O-H⋯N, N-H⋯O and O-H⋯O hydrogen bonds into a three-dimensional network.

The reaction of aqueous solutions of amino-guanidine hydrogennitrate and acetyl-acetone produces the title pyrazole salt, C(7)H(18)N(8) (2+)·2NO(3) (-). The crystal structure is stabilized by a complex N-H⋯O hydrogen-bonding network. The difference in the engagement of the two nitrate anions in hydrogen bonding is reflected in the variation of the corresponding N-O bond lengths.

The cation of the salt, C(18)H(18)N(2)O(2) (2+)·2NO(3) (-), lies about a twofold rotation axis. The pyridinium ring is almost coplanar with the phenyl-ene ring [dihedral angle between rings = 5.69 (9)°]. The crystal structure shows π-π stacking inter-actions [centroid-centroid distance = 3.70 (1) Å] between the pyridinium rings and the phenyl-ene rings, generating a linear chain structure. The ...

In the title compound, C(10)H(16)N(4) (2+)·2NO(3) (-), the organic cation is located around an inversion centre. The imidazolium ring forms a dihedral angle of 62.7 (3)° with the plane defined by the C atoms of the -(CH(2))(4)- aliphatic linker. Two anions bind to the cation via three-centre N-H⋯O hydrogen bonds and thus discrete hydrogen-bonded ion triples are formed. The nitrate is approximat...

(i= 1 . 2, . . .) such that the intersection n A, contains a perfect subset i=1 (and is therefore of power 2No) . They asked for what Hausdorff measure functions (k(i) is it possible to choose the subsequence to make the intersection set (1 A„,, of positive -measure . In the present note We show that the strongest possible result in this direction is true . This is given by the following; theor...

In the title molecular salt, C(7)H(20)N(2) (2+)·2NO(3) (-), the crystal structure exhibits an unusual back-to-back paired double-stacked packing arrangement culminating in an overall double zigzag pattern of the dications. The nitrate anions form a ring around one pair of double-stacked dications. An intricate three-dimensional N-H⋯O and N-H⋯(O,O) hydrogen-bonding network exists in the crystal ...