Infinite groups with Abelian centralizers of involutions

The article contains two characterizations of projective linear groups PGL₂(P) over a locally finite field P of characteristic 2: the first is defined in terms of permutation groups, and the second, in terms of a structure of involution centralizers. One of the two is used to prove the existence of infinite groups which are recognizable by the set of their element orders. In memory of Viktor A. Gorbunov Supported by RFFR grant No. 99-01-00550. Translated fromAlgebra i Logika, Vol. 39, No. 1, pp. 74–86, January–February, 2000.     

Frobenius Groups Generated by Quadratic Elements

An automorphism of a group X is said to be quadratic if there exist integers and such that for any . If is a Frobenius group then an element is said to be quadratic if induces, by conjugation in the core of , a quadratic automorphism. By definition, a group H acts on a group F freely if for and only with or . It is proved that a Frobenius group generated by two quadratic elements is finite and its core is commutative. In particular, any Frobenius group generated by two elements of order at most 4 is finite. Also we argue that a Frobenius group with finitely generated soluble core is finite. The results mentioned are used to show that a group acting freely on an Abelian group is finite if it is generated by elements of order 3, and the order of a product of every two elements of order 3 in is finite.     

Oriented immobilization of chymotrypsin by use of suitable antibodies coupled to a nonporous solid support.

In order to eliminate the kinetic limitation of chymotryptic hydrolysis of proteins due to diffusion, nonporous hydroxyalkyl methacrylate solid support was developed and used for oriented immobilization of chymotrypsin by means of suitable polyclonal antibodies. Nonporous microspheres were prepared by dispersion copolymerization of 2-hydroxyethyl methacrylate and ethylene dimethacrylate in an alcohol-toluene mixture stabilized with cellulose acetate butyrate. The resulting particles were 1.2 microm in diameter and possessed narrow size distribution. After modification with adipic acid dihydrazide they contained 2 micromol of reactive groups available for coupling of anti-chymotrypsin antibodies. Prepared immunosorbent adsorbed 166.7 microg of chymotrypsin per 1 g of dry carrier. Immobilized chymotrypsin retained practically 100% of its native proteolytic activity. Kinetic parameters of catalysis by chymotrypsin immobilized via this way were improved due to the good steric accessibility of the enzyme active site for high-molecular-mass substrates, when digestion of proteins in batch experiments was used.     

A new characterization of A 5

Let G be a group and τ _e (G) the set of numbers of elements of G of the same order. In this paper, by τ _e (G), we give a new characterization of A ₅, where A ₅ is the alternating group of degree 5. We get the theorem following: Theorem. Let G be a group, ${G\cong A_5}$ if and only if τ _e (G) = τ _e (A ₅) = {1, 15, 20, 24}.     

Nonlinear concave spiral autowaves and their applications

Works devoted to concave spiral autowaves are reviewed. Concave spiral phase autowaves do not transfer energy in self-oscillating active media. Concave spiral autowaves that transfer energy are predicted and found in certain inhomogeneous active media. Ways of studying them mathematically are developed. Applications of spiral concave autowaves that transfer energy in different natural processes (in physics, chemistry, hydrodynamics, biology, and meteorology) are considered.     

Mass spectrometer with a multichannel ion detector based on microchannel plates

Position sensitive detectors based on microchannel plates were introduced in a mass spectrometer. With the help of this multichannel ion detector, the measurement time and errors are reduced significantly.