A New Look at the Burnside-Schur Theorem

The famous Burnside–Schur theorem states that every primitivefinite permutation group containing a regular cyclic subgroupis either 2-transitive or isomorphic to a subgroup of a 1-dimensionalaffine group of prime degree. It is known that this theoremcan be expressed as a statement on Schur rings over a finitecyclic group. Generalizing the latter, Schur rings are introducedover a finite commutative ring, and an analogue of this statementis proved for them. Also, the finite local commutative ringsare characterized in permutation group terms. 2000 MathematicsSubject Classification 20B10, 20B15, 05E99.     

Kinetics of luminescence of CsI single crystals scavenged by Y3+

CsI single crystals were grown from the melt scavenged by Y³⁺ (YCl₃) addition in 6.7·10⁻⁴–6.7·10⁻³ mol·kg⁻¹ range. The addition of the scavenger amounts comparable with the total concentration of the oxygen‐containing admixtures in molten CsI results in complete destruction of the latter. Because of this, the intensity of the band with a maximum at 2.8 eV in radioluminescence spectra caused by the oxygen‐containing admixtures (anion vacancies) considerably decreases, and the fraction of the slow 2μs‐component corresponding to these admixtures becomes lower than 0.01 (0.007). The addition of larger quantities of YCl₃ leads to the appearance of a wide band with a maximum at 2.8 eV caused by cation vacancies, and the intensity of the slow 2μs‐component increases to 0.02. The maximum ratio of two faster components with the decay constants equal to 7 and 30 ns reaches 0.65:0.33 at Y³⁺ concentration in CsI melt equal to 6.7·10^‐3 mol·kg^‐1, the effective luminescence time of fastest components is ca 14 ns. The dependence of the ‘Fast/Total ratio’ on Y³⁺ concentration passes through its maximum (0.81) corresponding to the equivalence of Y³⁺ and O²⁻ concentrations in the growth CsI melt.     

On Schurity of Finite Abelian Groups

A finite group G is called a Schur group, if any Schur ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. Recently, the authors have completely identified the cyclic Schur groups. In this article, it is shown that any abelian Schur group belongs to one of several explicitly given families only. In particular, any noncyclic abelian Schur group of odd order is isomorphic to ?₃ × ?_{3 ^k} or ?₃ × ?₃ × ? _p where k ≥ 1 and p is a prime. In addition, we prove that ?₂ × ?₂ × ? _p is a Schur group for every prime p.     

Ionic polymerization in an electric field and consequences of the spatial redistribution of growing macroions and counterions

Reaction mixtures in which polymerization processes proceed are investigated both in an electric field and under classical conditions. The observed kinetic effects are explained using a model concept of the primary contribution to the revealed field effects from the dissociation of ion pairs due to the spatial redistribution of ions. This model may be applied to both cationic and anionic polymerization processes.     

Isomorphism of Coloured Graphs with Slowly Increasing Multiplicity of Jordan Blocks

n -vertex edge coloured graphs with multiplicity of Jordan blocks bounded by k can be done in time . Received: November 29, 1994     

Copolymerization of glycols with the divinyl ether of n-acetyldiethanolamine

Conclusions The migration copolymerization of the divinyl ether of N-acetyldiethanolamine and a number of glycols to give polyether amines containing acetal groups was investigated.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2577–2578, November, 1969.