On Transitive Permutation Groups with Primitive Subconstituents

Let G be a transitive permutation group on a set such that,for , the stabiliser G induces on each of its orbits in \{}a primitive permutation group (possibly of degree 1). Let Nbe the normal closure of G in G. Then (Theorem 1) either N factorisesas N=GG for some , , or all unfaithful G-orbits, if any exist,are infinite. This result generalises a theorem of I. M. Isaacswhich deals with the case where there is a finite upper boundon the lengths of the G-orbits. Several further results areproved about the structure of G as a permutation group, focussingin particular on the nature of certain G-invariant partitionsof . 1991 Mathematics Subject Classification 20B07, 20B05.     

IR and <Superscript>31</Superscript>P NMR spectroscopic study of complexation of carbamoyl methyl phosphinates with U<Superscript>VI</Superscript> and Th<Superscript>IV</Superscript> in nitric acid solutions

The composition of complexes formed upon the extraction of U^VI and Th^IV nitrates with O-n-nonyl(N,N-dibutylcarbamoylmethyl) methyl phosphinate (L) from solutions of nitric acid without additional solvent was determined by ³¹P NMR spectroscopy. The structures of the complexes formed were studied by IR spectroscopy. Uranium(VI) is extracted from 3 and 5 M solutions of HNO₃ as the [UO₂(L)₂(NO₃)₂] complex, while thorium(IV) is extracted from 5 M HNO₃ as the [Th(L)₃(NO₃)₃]⁺·NO ₃ ⁻ complex. In both cases, ligand L has bidentate coordination. Ligand L contacts with 3 and 5 M nitric acid to form adducts L·HNO₃ and L· (HNO₃)₂, respectively. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2460–2464, November, 2005.     

Implementing Brouwer’s database of strongly regular graphs

Andries Brouwer maintains a public database of existence results for strongly regular graphs on \(n\le 1300\) vertices. We have implemented most of the infinite families of graphs listed there in the open-source software Sagemath (The Sage Developers, http://www.sagemath.org), as well as provided constructions of the “sporadic” cases, to obtain a graph for each set of parameters with known examples. Besides providing a convenient way to verify these existence results from the actual graphs, it also extends the database to higher values of n.     

Nitrogen derivatives of pinenes possessing the properties of plant retradants

New nitrogen derivatives possessing the activity of plant growth regulators have been synthesized from the readily available natural terpenoids α- and β-pinenes.