Volume 11, Issue 4

Anatoly Ivanovitch Maltsev
(the 100th anniversary)

This issue is dedicated to the 100th anniversary of the great mathematician Anatoly Ivanovitch Maltsev (1909-1967), the founder of the modern novosiberian school of mathematical logic and algebra.

Article (rus.) - [pdf] [zip-pdf]

On some properties of extensions of commutative unital rings
Danchev P. V.
MSC (2000): 13B25, 13B02, 16N40.

We find necessary and sufficient conditions for the ring R[α]   to be either a field or a domain whenever R   is a commutative ring with 1 and α   is an algebraic element over R . This continues the studies started by Nachev (Compt. Rend. Acad. Bulg. Sci., 2004) and (Commun. Alg., 2005) as well as their generalization due to Mihovski (Compt. Rend. Acad. Bulg. Sci., 2005).

Article (eng.) - [pdf] [zip-pdf]

Local finiteness of some groups with given element orders
Zhurtov A. Kh., Mazurov V. D.

We find some sufficient conditions of local finiteness for a group with elementary abelian centralizers of involutions.

Article (rus.) - [pdf] [zip-pdf]

On intersections of Sylow 2-subgroups in finite groups, I
Zenkov V. I., Makosiy A. I.

In a finite simple group with simple socle of Lie type over a field of order 3, where Lie rank doesn't exceed 4, we found the lower bound for the number of orbits under the conjugation action of the fixed Sylow 2-subgroup on the set of Sylow 2-subgroups that intersect the fixed on the unit subgroup. Some computer calculations are also used.

Article (rus.) - [pdf] [zip-pdf]

Transvections in the overgroups of a non-split maximal torus
Koibaev V. A., Shilov A. V.

In this paper we research intermediate subgroups of general linear group GL(n,k)   of dimension n   over an arbitrary field k   containing non-split maximal torus associated with extension of main field k   dimension n . We prove that if overgroup of non-split maximal torus contained one-dimensional transformation it would contain elementary transvections at least in two positions of any column and any row. We also prove that if extension of field k   was prime overgroup of non-split maximal torus containing one-dimensional transformation would contain elementary transvections in each position.

Article (rus.) - [pdf] [zip-pdf]

On recognizability by spectrum of finite simple orthogonal groups, II
Kondrat'ev A. S.

The recognizability by spectrum of a class of finite simple o rthogonal groups with disconnected prime graph is studied.

Article (rus.) - [pdf] [zip-pdf]

On automorphisms of strongly regular graph with parameters (95,40,12,20)
Makhnev A. A., Chuksina N. V.

The structure of fixed-point subgraphs of automorphisms with prime orders of strongly regular graph with parameters (95,40,12,20)   is described. As a corollary it is proved that the point graph of partial geometry pG 2 (4,9)   is not vertex-transitive.

Article (rus.) - [pdf] [zip-pdf]

Generating triples of involutions of linear groups of dimension 2 over ring of integer
Nuzhin Ya. N., Timofeenko I. A.

For linear groups of dimension 2 over the integers we found the minimum number of generating triples of involutions which product is equal to 1. It is established that PG L 2 (ℤ)   is generated by three involutions and two of them commute, while G L 2 (ℤ)   doesn't possess such involutions.

Article (rus.) - [pdf] [zip-pdf]

The solution of the Rashevsky problem
Hubezhti I. A.

In this paper we give the description of the infinite projective plane ω 3 * , in which the configuration theorem 8 3   holds projectively, by so called Rashevsky plane. We prove that the plane is Moufang and we positively solve the Rashevsky problem: "Is the plane ω 3 * Moufang?".

Article (rus.) - [pdf] [zip-pdf]