OctoberDecember, 2009
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 (19091967),
the founder of the modern novosiberian school of mathematical
logic and algebra.
Article (rus.)  [pdf] [zippdf]
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] [zippdf]
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] [zippdf]
On intersections of Sylow 2subgroups 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 2subgroup on the
set of Sylow 2subgroups that intersect the fixed on the unit
subgroup. Some computer calculations are also used.
Article (rus.)  [pdf] [zippdf]
Transvections in the overgroups of a nonsplit 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 nonsplit maximal torus associated with extension of
main field
k
dimension
n
. We prove that if overgroup of
nonsplit maximal torus contained onedimensional 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 nonsplit maximal
torus containing onedimensional transformation would contain
elementary transvections in each position.
Article (rus.)  [pdf] [zippdf]
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] [zippdf]
On automorphisms of strongly regular graph with parameters
(95,40,12,20)
Makhnev A. A., Chuksina N. V.
The structure of fixedpoint 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 vertextransitive.
Article (rus.)  [pdf] [zippdf]
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] [zippdf]
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] [zippdf]
