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Let Gbe a finite group, and let Aand Bbe, respectively, an Abelian and a nilpotent subgroup in G. In the present paper, we complete the proof of the theorem claiming that there is an element gof Gsuch that the intersection of Awith the subgroup conjugate to Bby gis contained in the Fitting subgroup of G.

Abstract: Kinetic features of adsorption-desorption processes for a nitrogen and oxygen mixture of gases, nitrogen and water vapor at the surface of finely-dispersed amorphous powders of brown and black boron used to synthesize metal borides are studied. The different adsorption-chemical activity of amorphous brown and black boron powders towards the main components of an air atmosphere is determined. It is shown that the original boron, apart from hard impurity compounds, may carry at the surface gaseous constituents with a capacity to change the physicochemical parameters of the system in the reaction zone, and to affect the phase composition and quality of the product obtained.

Abstract: We used the continuous weighing method to study the oxidation kinetics in air for TiN specimens pressed and sintered from nanocrystalline powders with particle size ≤55 nm. Oxidation was carried out at 500–1000 C for 240 min. By comparing with the oxidizability of compact titanium, we estimated the total reaction surface S of the porous specimens as a function of their oxidation conditions. The mass of absorbed oxygen Δm was calculated from the mass gain ΔP, taking into account the volatile component N2. We have shown that the maximum mass gain Δm at 600 C is due to reaction of oxygen with the largest reaction surface. Within 120 min, external pores close up, S decreases, and then a continuous oxide layer forms in which diffusion of oxygen is slowed down. At 700–800 C, the process of closing up of the pores is activated, and S decreases by an order of magnitude compared to 600 C. After the first 40–50 min, a continuous oxide film forms and virtually no further mass gain occurs. As the temperature increases, the oxidation rate increases. At 900 C, the reaction surface becomes equal to the external surface of the specimen, but the thickness of the scale increases linearly. We hypothesize that for T > 850 C, counterdiffusion of titanium ions is superimposed on diffusion of oxygen.

Abstract: In Theorem 1, letting p be a prime, we prove: (1) If G=Sn is a symmetric group of degree n, then G contains two Sylow p-subgroups with trivial intersection iff (p, n) ∉ {(3, 3), (2, 2), (2, 4), (2, 8)}, and (2) If H=An is an alternating group of degree n, then H contains two Sylow p-subgroups with trivial intersection iff (p, n) ∉ {(3, 3), (2, 4)}. In Theorem 2, we argue that if G is a finite simple non-Abelian group and p is a prime, then G contains a pair of Sylow p-subgroups with trivial intersection. Also we present the corollary which says that if P is a Sylow subgroup of a finite simple non-Abelian group G, then ‖G‖>‖P‖2.

Abstract: Using the basic theorem on the classification of finite simple groups, we answer one of the questions concerning the generation of finite groups by the class of conjugate Abelian subgroups.

he parameters of water vapor adsorption on the surfaces of powders and compacted powders (compacts) are compared with data on the variation of the electrical resistance of the same compacts in media with various water vapor contents. A study of the kinetic features of water vapor adsorption from the air indicated that powders with small specific surfaces adsorb water vapor and are saturated more rapidly than do powders with large specific surfaces, while their absolute moisture content is lower. The amount of water vapor adsorbed on the surface varies in the same way. The data are consistent with the results from porous structure studies. The rate of water vapor adsorption and the amount adsorbed increase for smaller pores, in which the water vapor condenses more quickly. Data on the specific surface of compacted and sintered materials, their porous structure and their adsorptivity of water vapor provide a basis for making a prior choice of technological parameters of the ceramic treatment so as to enhance the quality of humidity meters.

Abstract: The kinetic features and mechanism of reduction of γ-Fe2O3 in hydrogen in the presence of CaO as a getter for the gaseous reaction products was studied. Data were obtained on the kinetic constants, reaction rate, and evolution of surface area during the reaction. It was established that the getter has a favorable effect on the degree of dispersion of the reaction products.

Studies have been made on the kinetics of nickel oxide powder reduction by hydrogen in the presence of calcium oxide as a water vapor getter. The getter influences the reduction mechanism and the coalescence of the reduced metal as well as the growth of fresh surface. Data are presented on the fresh surface of the nickel powder formed in the presence of calcium oxide and in the absence of it as regards reduction kinetics.

Abstract: Using the classification of finite simple groups, we tackle problem 5.12 from the “Kourovka Notebook,” for G a finite group satisfying Op=1 for any prime p.

We have studied air oxidation (600–950°C) of TiFe alloy by the gravimetric method. We describe the oxidation process by a parabolic time law as well as an exponential temperature law. The weight increase isotherms have breaks, the two parts of the lines corresponding to a periodic increase in the rate constant at temperatures less than 800°C and a decrease at temperatures higher than 800°C. The activation energy also increases above 800°C, and the difference between the oxidizability of TiFe and its analog TiNi decreases. The change in the oxidation mechanism for TiFe is hypothetically determined by the increase in the role of rutile in high-temperature oxidation, and the possibility of diffusion of titanium through interstitial positions of the rutile (TiO2) lattice, similar to previously studied oxidation.

Abstract: The influence of sintering temperature for ceramic humidity sensors based on nanophase zirconium dioxide with a specific surface of 110 m2/g on their adsorption and operation, and the change in their pore structure has been studied. It was also established that nanophase zirconium dioxide is very promising for ceramic humidity sensors. Optimum characteristics are obtained with sintering at 900–1100�C which provides a wide range of pores that are responsible for the sensitivity of humidity determination over the whole measurement range. The greatest sensitivity for high humidity values is obtained for samples sintered at 1100�C. It was established that the specific surface of samples differs little with sintering in the range 900–1100�C but it decreases markedly with sintering up to 1300�C.