On Linear Groups of Degree 2n Containing a Representation of the Special Linear Group of Degree n

Let n be an integer, n ≥ 2, and let a field P be a quadratic extension of an infinite field k. Regarding P as a k-vector space of dimension 2, we consider an n-dimensional P-vector space V as a 2n-dimensional k-vector space so the general linear group GL _n (P) acting on V is embedded in the group GL _2n (k). Let a field K be an algebraic extension of k. In this article, we determine overgroups of the special linear group SL _n (P) in the group GL _2n (K).     

Linear Groups of Degree 4 Over a Quaternion Division Ring that Contain the Special Unitary Group of a Skew-Hermitian Form with Maximal Witt Index

The paper describes subgroups of the general linear group GL ₄(D) over a quaternion division ring D that contain the special unitary group of degree 4 over a non-central subfield of D. The connections between these subgroups and the spinor groups of appropriate symmetric bilinear forms are established.     

On linear groups containing the commutator subgroup of an orthogonal group of index greater than 1

Minsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No. 5, pp. 15–21, September–October, 1992.     

On the surface viscosity at the boundary between phases

The equations of motion of the interphase boundary are considered. It is shown that the conditions at the surface separating the phases obtained in /1, 2/ by different methods, are identical. The study of the dynamics of the fluid-fluid interface was initiated by Bussinesq /3/ who postulated a linear relationship between the surface stress tensor T_β and the strain rate tensor S_β, assigning two viscosity coefficients to the surface, the dilatation coefficient k (the analog of volume viscosity) and the two-dimensional shear viscosity . In the three-dimensional coordinate system two of whose axes u¹ and usu2 coincide with the axes of any coordinate system at the surface and whose third axis u³ is perpendicular to the surface, his results have the form Tβ = [γ + (k - )θ]a_β + S_β , θ = a^βS_β, V_{, β} = r_{. β} — v_sb_β,      

Mössbauer studies of sublattice magnetization curves of ferromagnets with several species of characterizing ions

The paper gives a model of a local molecular field describing the magnetization curves in iron garnets separately according to magnetic sublattices. It takes account of the relation between the ion distribution over the lattice sites as well as the values of the local magnetic field and the parameters of the superexchange interaction in such materials. The relations obtained are compared with the data of Mössbauer and NMR spectroscopy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 83–88, June, 1979.