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D. N. Azarov, D. V. Goltsov
Virtually residually p-finiteness of free product of two groups with
finite amalgamated subgroups Let G be a free product of groups A and B with amalgamated finite subgroups H and K. It is proved that if A and B are virtually residually finite p-groups, then G is virtually residually a finite p-group.
D. N. Azarov, A. V. Rozov
On the residual finiteness of free product of soluble groups of finite rank
with normal amalgamated subgroups The necessary and sufficient condition of residual finiteness for free product of soluble groups of finite rank with normal amalgamated subgroups is obtained.
A. S. Belov
On one sequence of nonnegative trigonometric polynomials For every positive integer n let Vn be unique extremal trigonometric polynomial of the extremal problem on the minimum of the constant term of even nonnegative trigonometric polynomial of the degree n, with all coefficients without constant term not less 1. In the article the zeros of the trigonometric polynomial Vn and some properties of the sequence of the polynomials {Vn(x)}n=1∞ are studied.
D. V. Goltsov, N. I. Yatskin
Classes of groups and subgroup topologies An abstract class C of groups defines the so-called co-C topology on an arbitrary group. This topology is generated by the family of co-C normal subgroups. Some important concepts and results of the combinatorial group theory (CGT) have adequate topological interpretations. Our work follows in some detail this well known "topologizing trend" in CGT. In particular we clarify the topological sense of the Gruenberg condition in the definition of a root class of groups and investigate some criterions of being co-C hereditary for subgroups.
Ye. A. Ivanova, D. I. Moldavanskii
On the conjugacy separability in the class of finite groups for Baumslag - Solitar
soluble groups It is shown that any group <a, b; a-1ba = bk> where integer k differs from zero and ±1 is not conjugacy separable by finite \pi-groups for every set \pi consisting of two prime numbers.
S. V. Kolesnikov
On existence of solution of one extremal problem in the space H1 A sufficient condition of existence for extremal function of bounded functionals in the space H1 is proved. This condition is used for a proof of a certain proposition about badly approximable functions in H∞.
Ye. D. Loginova, D. I. Moldavanskii
On the residuality a finite p-groups of a commuted HNN-extension The necessary and sufficient condition for commuted HNN-extension to be residually a finite p-groups is obtained.
Ye. V. Sokolov
On applicability of A. I. Maltsev's algorithm to infinite group
presentations Groups with infinite recursive presentations are considered. Certain conditions are obtained which are sufficient to apply algorithms based on the idea of "finite reducibility" for solving algorithmic problems in such groups.
D. V. Turtin
Maximal classes of nonuniqueness of solution to the Cauchy problem for linear
equations We study linear partial differential equations with increasing coefficients in a half-plane. We establish maximal nonuniqueness of solutions to the Cauchy problem for these equations. The proof is based on a new estimation method for solution to the dual differential equation with a parameter.
S. I. Khashin
Basic properties of upper and lower Butcher's algebras For each Runge - Kutta method, we construct two graduated finite-dimensional commutative algebra with identity - the upper and lower Butcher's algebras. Their properties explain the algebraic meaning of Butcher equations. |
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