Profinite groups of finite cohomological dimension

Let 1→N→G→G/N→1 be a short exact sequence of profinite groups, and let p be a prime number. We prove that if G is of finite cohomological p-dimension n:=cd_p(G)<∞ and if the order of $\text{H}{}^{\mathrm{k}}\text{(N,}\text{F}{}_{\mathrm{p}}\text{)}$ is finite for k:=cd_p(N), the virtual cohomological p-dimension of G/N equals n?k. To cite this article: T. Weigel, P. Zalesskii, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Reaction of pentachloropyridine N-oxide with potassium hydrogen sulfide

Depending on the conditions, the reaction of pentachloropyridine N-oxide with potassium hydrogen sulfide leads to the N-oxide of the potassium salt of 3,4,5,6-tetrachloropyridin-2-thiol or the dipotassium salt of 3,4,5-trichloropyridine-2,6-dithiol, which are converted by the action of dimethyl sulfate into the corresponding methylthio derivatives. Oxidation of the latter has given sulfones. It has been shown that for these sulfones,reactions with nucleophilic reagents take place at the methylsulfonyl group and not at the chlorine atoms.     

On simple periodic linear groups— Dense subgroups,permutation representations,and induced modules

We determine the Zariski-dense subgroups of Chevalley groups and their twisted analogues over infinite algebraic extensions of finite fields. It turns out that these are essentially forms of the same group (possibly becoming twisted) over smaller infinite fields. It follows from our classification that if is a simple algebraic group over the algebraic closure of a finite field, then a dense subgroup of can never be maximal, and so the maximal subgroups of are necessarily closed. It follows that Seitz’s determination of the closed maximal subgroups of actually gives all the maximal subgroups. It also enables us to prove that ifG is a simple Chevalley group or twisted type over an infinite algebraic extension of a finite field, then in every non-trivial permutation representation ofG, every finite subgroup has a regular orbit. It follows that every non-trivial permutation module forG over a fieldk iskG-faithful. This is relevant to a programme of studying ideals in group rings of simple locally finite groups. To John Thompson in recognition of his many outstanding contributions to group theory     

Invariant ideals of abelian group algebras under the multiplicative action of a field. I

Let be a division ring and let be a finite-dimensional -vector space, viewed multiplicatively. If is the multiplicative group of , then acts on and hence on any group algebra . Our goal is to completely describe the semiprime -stable ideals of . As it turns out, this result follows fairly easily from the corresponding results for the field of rational numbers (due to Brookes and Evans) and for infinite locally-finite fields. Part I of this work is concerned with the latter situation, while Part II deals with arbitrary division rings.

     

Composition-induced transition of spin-modulated structure into a uniform antiferromagnetic state in a Bi<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>La<Subscript>x</Subscript>FeO<Subscript>3</Subscript> system studied using <Superscript>57</Superscript>Fe NMR

By analyzing the NMR line shape, the transformation of a spatially spin-modulated magnetic structure in BiFeO₃ into an ordinary spatially uniform structure of the LaFeO₃ orthoferrite in Bi_1?xLa_xFeO₃ solid solutions is studied. The measurements are made using a spin-echo technique at temperatures of 77 and 4.2 K on ceramics with compositions x=0, 0.1, 0.2, 0.61, 0.9, and 1.0 enriched by the ⁵⁷Fe isotope. It is shown that the spin-modulated structure disappears near the concentration x=0.2, which corresponds, according to the published data, to the phase transition with a change in the unit-cell symmetry R3c → C222. A formula is obtained describing the NMR absorption line shape for the spin-modulated structure with account of local line-width. Theoretical spectra adequately describe the evolution of the experimental spectrum in the concentration range 0≤x≤0.2. Highly nonuniform local magnetic fields in the intermediate compositions make it impossible to detect NMR signals in a sample with x=0.61. A uniform magnetic structure characterized by a single narrow line arises in the range of existence of a phase with the symmetry Pnma typical of the pure orthoferrite LaFeO₃.     

A geometric characterization of free formations of profinite groups

Minsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 2, pp. 73–84, March–April, 1989.     

Magnetic properties of multiferroics-semiconductors Eu(1-x)Ce(x)Mn2O5

Studies of magnetization, magnetoresistance, and magnetic oscillations in semiconductor-multiferroics Eu(1-x)Ce(x)Mn2O5 (x = 0.2-0.25) (ECMO) at temperatures ranging from 5 to 350 K in magnetic fields up to 6 T are presented. It is shown that phase separation and charge carrier self-organization in the crystals give rise to a layered superstructure perpendicular to the c axis. An effect of magnetic field cycling on the superstructure, magnetization, and magnetoresistance is demonstrated. X-ray diffraction studies of ECMO demonstrating the effect of magnetic field on the superstructure are presented. The de Haas-van Alphen magnetization oscillations in high magnetic fields and the temperature-induced magnetic oscillations in a fixed magnetic field are observed at low temperatures. Below 10 K the quantum corrections to magnetization due to the weak charge carrier localization in 2D superlattice layers occur. It is shown that at all the temperatures the Eu(1-x)Ce(x)Mn2O5 magnetic state is dictated by superparamagnetism of isolated ferromagnetic domains.     

Antiferromagnetic resonance in Bi2CuO4

Magnetic resonance of the low-frequency spin-wave branch in the Bi₂CuO₄ antiferromagnet with an easy-plane anisotropy has been studied. Angular, frequency, and temperature dependences of the position and width of the antiferromagnetic resonance (AFMR) line have been measured. Our measurements combined with earlier data [H. Ochta, K. Yoshida, T. Matsuya, T. Nanba, M. Motokawa, K. Yamada, Y. Endon, and S. Hosoya, J. Phys. Soc. Jpn. 61, 2921 (1992); E. W. Ong, G. H. Kwei, R. A. Robinson, B. L. Ramakrishna, and R. B. von Dreele, Phys. Rev. B 42, 4255 (1990) [ have allowed us to determine anisotropy constants of this material and to account for the unusual character of its static susceptibility anisotropy. The AFMR line shifts to the high-field side and broadens in a temperature range of 10–15 K, and the cause of this has remained unclear. In the low-temperature range the line shows a hysteresis corresponding to a static field magnitude several times as large as the spin-flop field. The position and width of the AFMR line depend sensitively on the sample preparation technique. Zh. éksp. Teor. Fiz. 113, 2244–2255 (June 1998)