Present number of the journal is devoted to light memory of the outstanding matematicians -- the Academicians S.A. Chunikhin, D.A. Suprunenko, and V.G. Sprindzuk. Its issue has connected with 90-th Anniversary of the Birthday of Sergei Antonovich Chunikhin, 80-th Anniversary ot the Birthday of Dmitrii Alekseevich Suprunenko, and 60-th Anniversary of the Birthday of Vladimir Gennadievich Sprindzuk. The subjects of the number is rather various (final groups, formations, group of matrixes, the theory of representations, elliptic curves, combinatorics, Diophantine equations and Diophantine approximations) and at the same time is uniform enough: all specified directions are united within the framework of ancient and eternally young science - algebra and theory of numbers. The material of the number contains mainly theoretical results, however alongside with them the reader will find both applications in the field of cybernetics and computer science. The number consists of three sections representing the appropriate scientific schools. The personal contribution of the Academicians S.A. Chunikhin, D.A. Suprunenko, and V.G. Sprindzuk in a mathematical science, and also in development of the scientific schools created by them is covered in details in clauses opening these sections. We shall note only the circumstance that Sergei Antonovich, Dmitrii Alekseevich and Vladimir Gennadievich were distinguished the nobleness, high culture and intelligence, sincerity and goodwill. They were united by an indefatigable care of that mathematical investigations in Belarus would developed at the highest level. Their fruitful activity in this direction is a worthy sample for present and future generations of the researchers. Using a case, we express gratitude to the Editor-in-Chief of the journal the Academician V.S. Burakov which initiated the edition of the present number, and also members of Editorial Board for support and help in preparation of the number.
Шеметков Л.А.
Сергей Антонович Чунихин (1905--1985). С. 6--7
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Safonov V.G
On solvable local formations of nilpotent defect 3. pp. 8--12
Summary: In this paper we give a description for solvable local formations of finite groups of nilpotent defect 3.
Jeraden Jehad, Skiba A.N.
Partially local formations with systems of inherited subformations. pp. 13--16
Summary: In this work it has been proved that all p-local subformations of the p-local formation F are S-closed if and only if F Í Np N.
Selkin V.M.
On minimal local normally inherited nonformations. pp. 17--20
Summary: In this paper we give a description of minimal local normally inherited non N-formations, where N is a normally inherited local formation of classical type.
Monakhov V.S.
On the product of two groups with cyclic subgroups of index 2. pp. 21--24
Summary: A finite group G = AB, where A and B contain cyclic subgroups of indexes £ 2, is considered. It is proved that such groups are solvable, their 2-length does not exceed 2 and p-length is equal to 1.
Semenchuk V.N.
On a problem of formation theory. pp. 25--29
Summary: In this paper we give a new characterization of formation F with Shemetkov's condition. Formation F satisfies Shemetkov's condition if each minimal non-F-group is either Schmidt's group or is of prime order.
Бураков В.С., Гайшун И.В., Танаев В.С. и др.
Дмитрий Алексеевич Супруненко (1915--1990). С. 30--32
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Konjukh V.S.
On linear nilpotent groups of nilpotency class 2. pp. 33--35
Summary: Necessary and sufficient conditions under which the set of irreducible nilpotent subgroups in GL(n, P) of nilpotency class 2 consists of a finite number of conjugacy classes are obtained.
Volvachov R.T.
Linear representativity of HNN-extensions of finite cyclic groups. pp. 36--40
Summary: It is proved that every H N N-extensions of finite cyclic group, i. e. group Gn, d, l = (a, t; an = e, t-1 ad t = adl) with d, l -- natural numbers, d/n, (l, n/d) = 1, has a faithful linear representation of a finite degree over some field of characteristic 0.
Zalesskii A.E.
Eigenvalues of prime order elements in projective representation of alternating groups. pp. 41--43
Summary: Let j be a complex projective or ordinary irreducible representation of the alternating group An, n > 7, and g Î An an element of prime order p > 2. Suppose that dim j > 1 and that the matrix j(g) has less than p distinct eigenvalues. We prove that if j is ordinary, then n = p and dim j = p - 1, and if j is projective, then p = 3 or 5 and j is a basic representation of An of dimension 2k-1 where k = n/2 if n is even, and k = (n + 1)/2 if n is odd.
Suprunenko I.D.
Properties of unipotent elements in irreducible representations of the classical groups with p-large highest weights. pp. 44--48
Summary: Irreducible representations of the classical algebraic groups in characteristic p > 0 with highest weights large enough with respect to p are considered. A notion of a p-large representation determined in terms of the highest weight and the maximal root is introduced. For each type of the classical algebraic groups a linear function f such that the image of an element of order p in a p-large representation of the group of lank r of this type has at least f(r) Jordan blocks of size p is explicitly indicated.
Yuferev V.P.
On the problem of classification of nilpotent linear groups. pp. 49--53
Summary: Absolutely irreducible nilpotent linear groups over a field that are maximal among the groups of their nilpotency class are considered. In some cases the canonical form and the complete classification up to the conjugacy of these groups are given.
Melnikov O.V.
Quotient groups of profinite groups with Poincare duality. pp. 54--58
Summary: It is proved that if p¥ divides the index of a subgroup H of a profinite Poincare duality group G of dimension n (PDn-group for brevity), then cdpH £ cdp G - 1. Conditions are found under which the maximal pro-solvable pro-p-quotient group of a PD2-group is PD2-group, too.
Goglev V.V., Yanchevskii V.I.
Two-primary torsion of Brauer groups of local elliptic curves with additive reduction. pp. 59--63
Summary: The presentation of two-primary torsion part of the Brauer group of local non-dyadic elliptic curve with additive reduction by means of unramified division algebras is determined.
Guletskii V.I.
Invariants of simple algebras over function fields of principal homogeneous spaces of elliptic curves over number fields. pp. 64--68
Summary: The obstruction group for realization of characters systems, satisfying reciprocity law, as sets of local invariants of elements of Brauer group of k-rational functions on principal homogeneous spaces of elliptic curves over number field k is calculated.
Burkard R.E., Demidenko V.M., Rudolf R.
Generalized Supnik's and Kalmanson's conditions and their applications to symmetric and nonsymmetric traveling salesman problems. pp. 69--74
Summary: This paper proposes sufficient conditions for the traveling salesman problem that generalize well-known Supnik's and Kalmanson's conditions for the symmetric and asymmetric cases. In particular, two new classes of so-called generalized Supnik's matrices and Kalmanson's matrices are introduced, for which the cycles (1, 3, 5,.. .,6, 4, 2) and (1, 2,... , n - 1, n) are solutions of the traveling salesman problem.
Babaitsev A.Yu., Tyshkevich R.I.
k-Dimensional graphs. pp. 75--81
Summary: k-Dimensional graphs are studied. It is proved that the class of k-dimension graph coincides with the class of line graphs of k-coloring hypergraphs. A characterization of this class in terms of clique covering of a graph is given. It is proved that recognition of the property "k-dimension" with fixed k > 2 is a NP-complete problem.
Emelichev V.A., Gladkii A.A., Yanushkevich O.A.
On multicriteria problems of finding of lexicographical optimum. pp. 82--86
Summary: It is shown that any lexicographic optimum of multicriteria problems with a finite set of vector estimates can be found by the algorithm of linear convolution of particular criteria.
Melnikov O.I., Radchuk A.A., Radchuk V.Ya.
The transitive closure of a digraph. pp. 87--88
Summary: In the paper an algorithm of complexity O(|V H|2) for constructing the transitive closure of a digraph H is presented.
Shlyk V.A.
Polytopes of partitions of integers. pp. 89--92
Summary: The sets of nonordered partitions of positive integer numbers are considered from the polyhedral point of view. It is proved that the dimension of polytope Pn of all partitions of number n is n - 1 and that the polytope P2n almost wholly enfolds Pn, or more precisely: only one of the entire scope of vertices of Pn indices a vertex of P2n. It is also proved that the polytope Pn can be viewed as a special case of polyhedra on partial algebra, the construction of which was proposed by the author earlier, and therefore all non-trivial facets of Pn satisfy the subadditive characterization property.
Martynchik V.N.
The cone of convex directions for a polygonal region. pp. 93--97
Summary: The convexity with respect to a given direction set is considered. A relation of the cone of convex directions for a polygonal region to the structure of its border is under research. An algorithm for computing the cone is developed.
Matveev G.V.
Primitive binary matrices. pp. 98--100
Summary: Some results about bounds on sizes and structure of binary absolutely primitive matrices are presented.
Lepin V.V.
Solving some problems in the class of graphs with a restricted front-width. pp. 101--105
Summary: The class of graphs with a restricted frontwidth is considered. Methods to obtain solutions to a number of well-known problems for this class are developed.
Бураков В.С., Гайшун И.В., Берник В.И.
Владимир Геннадьевич Спринджук (1936--1987). С. 106--108
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Bernik V.I., Morozova I.M.
R.Baker's conjecture and regular sets of algebraic numbers with a restriction on the derivative. pp. 109--113
Summary: It is proved the sets of real numbers with the same type in Mahler's and Koksma's classification can have the different Hausdorff dimension.
Kovalevskaya Ye.I.
Multidimensional extremal surfaces of Sprindzuk and the Hausdorff dimension. pp. 114--116
Summary: It is the bothside estimates fur the Hausdorff dimension r of the set M(v) Ì G, where G is an extremal smooth manifold, G Ì Rm+n, m > n2 + n - 1, v > 1/(m + n), and M(v) consists of the simultaneous well approximable points with index v (in the sense of Metric Theory of Diophantine Approximation):
1/(m+ n)(v + 1) £ r £ (m2 + m(n + 1))/(m + n)(v + 1).
Trelina L.A.
On the hyperelliptic diophantine equation. pp. 117--120
Summary: An estimate for the heights of K-rational solutions to f(x) = Ay2 in terms of the norms of their denominators and some applications are considered.
Dombrovskii I.R.
Diophantine approximations on the Cartesian product of curves and the Hausdorff dimension. pp. 121--124
Summary: Upper and lower estimates for the Hausdorff dimension of the set of well approximable points of the surface
Z(x, y) = P(x) + Q(y), where P, Q Î Z[x] are obtained.
Beresnevich V.V.
On the relation between orders of approximations of points on planar curves and the vector of derivatives. pp. 125--129
Summary: A metric theorem on approximations of planar smooth curve points and their vector of derivatives is proved.
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Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: 7 ноября 2006 г.
Создана при участии Игнатия И. Корсака
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Копирайт © 1996 Издательство "Беларуская навука"
