Subgroups,of Chevalley groups over a locally finite field,defined by a family of additive subgroups

It is proved that every elementary carpet of nonzero additive subgroups which is associated with a Chevalley group of a Lie rank exceeding one over a locally finite field coincides, up to conjugation by a diagonal element, with a carpetwhose additive subgroups are equal to some chosen subfield of the ground field. A similar result is obtained for a full matrix carpet (a full net).     

Weyl groups as Galois groups of a regular extension of the field ℚ

For a finite group G, Gal_T(G) denotes the property that there exists a regular Galois extension of the rational function field ℚ(T) over the field of rationals ℚ, with a Galois group G. This property is established to be satisfied by all Weyl groups except the type F₄, from which it follows that it holds also for Chevalley groups C₃(2) and D₄(2). Translated fromAlgebra i Logika, Vol. 34, No. 3, pp. 311-315, May-June, 1995.     

On Strong Reality of Finite Simple Groups

In this paper we shall consider the following problem. Which finite simple groups have the property: any element is inverted by an involution?     

Intermediate subgroups in the chevalley groups of type B l , C l , F 4, and G 2 over the nonperfect fields of characteristic 2 and 3

We describe the intermediate subgroups in the Chevalley groups of type B _l , C _l , F ₄, and G ₂ over various fields of characteristic 2 and 3 in the case that the larger field is an algebraic extension of the smaller nonperfect field.     

Bruhat Decomposition for Carpet Subgroups of Chevalley Groups Over Fields

Algebra and Logic - Necessary and sufficient conditions for a Bruhat decomposition to exist in a carpet subgroup of the Chevalley group over a field defined by an irreducible closed carpet of...     

Defining Relations for the Carpet Subgroups of Chevalley Groups over Fields

The carpet subgroups admitting a Bruhat decomposition and different from Chevalley groups are exhausted by the groups lying between the Chevalley groups of type \( B_{l} \), \( C_{l} \), \( F_{4} \), or \( G_{2} \) over various imperfect fields of exceptional characteristic 2 or 3, the larger of which is an algebraic extension of the smaller field. Moreover, as regards the types \( B_{l} \) and \( C_{l} \), these subgroups are parametrized by the pairs of additive subgroups one of which may fail to be a field and, for the type \( B_{2} \), even both additive subgroups may fail to be fields. In this paper for the carpet subgroups admitting a Bruhat decomposition we present the relations similar to those well known for Chevalley groups over fields.

     

Lie rings defined by the root system and family of additive subgroups of the initial ring

The paper surveys mathematical models of magma flow in a volcanic conduit in the case of extrusive (nonexplosive) eruption that were developed in the group of dynamic volcanology at the Institute of Mechanics, Moscow State University, under the supervision of Professor A.A. Barmin. In the quasi-one-dimensional and two-dimensional formulations, the effect of crystallization, heat exchange, and viscous dissipation on the relationship between the magma discharge rate and the pressure difference between the magma chamber and atmosphere is analyzed. It is shown that there exist several steady-state solutions of the boundary value problem that differ in discharge rates by orders of magnitude. A transition between steadystate solutions may lead to cyclic variations in the magma discharge rate. Limitations of the hydraulic approach, which is based on the parameters averaged over the cross-section of a volcanic conduit, are revealed.     

Intermediate subgroups of chevalley groups over a field of fractions of a ring of principal ideals

Let K be a field of fractions of a principal ideal ring R and G_K be a Chevalley group (of normal type) over K. For each subring P ⊂ K, denote by G_P a subgroup of all elements of G_K with coefficients in P. Let M be intermediate between G_R and G_K, i.e., G_R ⊆ M ⊆ G_K. We prove that M=G_P for some intermediate subring P (R ⊆ P ⊆ K). Supported by RFFR grant No. 96-01-00409. Translated fromAlgebra i Logika, Vol. 39, No. 3, pp. 347–358, May–June, 2000.     

Levi Decomposition for Carpet Subgroups of Chevalley Groups Over a Field

It is proved that a carpet subgroup of a Chevalley group of type Φ over a field is a semidirect product whose kernel is defined by a unipotent carpet of type Φ, while the noninvariant factor is a central product of carpet subgroups each of which is defined by an irreducible subcarpet of type Φi for some indecomposable root subsystem Φ _i of Φ. The obtained result can be viewed as an analog of the Levi decomposition.