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D. N. Azarov
On the virtually residually p-finiteness of some soluble groups For some soluble groups the necessary and sufficient condition to be virtually residually a finite p-group is obtained.
D. N. Azarov, D. V. Goltsov
On the virtually residuality of generalized free products and HNN-extensions
of groups in some classes of finite groups Let K be a root-class of finite groups. 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 K-groups, then G is virtually residually a K-group. The similar result for HNN-extensions is proved.
A. S. Belov
On the localization of the zeros of some 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 localization of the zeros of the trigonometric polynomial Vn and asymptotic behavior some values which link with the polynomials {Vn(x)}n=1∞ are studied.
I. A. Varlamova, D. I. Moldavanskii
On the residually finiteness of Baumslag - Solitar groups For one-relator groups from the family of Baumslag - Solitar groups the conditions to be residually a finite \pi-groups and conjugacy separable by finite \pi-groups are considered.
A. S. Gudovschikova, Ye. V. Sokolov
Some residual properties of generalized free products of two groups Let C be a class of groups satisfying certain conditions. The sufficient condition is proved for a generalized free product of two groups to be residually C. The description of C-separable cyclic subgroups of this construction is also obtained.
L. N. Kuskovskii, S. A. Pletyukhina
On one type of hypercomplex functions In the finite-dimensional algebra, which defined by polynomial equation, the basis is constructed with a convenient multiplication law. The structure of the monogenic function and some applications are described.
A. V. Rozov
On the virtually residually p-finiteness of free product of finitely
generated nilpotent groups with normal amalgamated subgroups We prove that for any prime p the free product of two finitely generated nilpotent groups with normal amalgamated subgroups is a virtually residually finite p-group.
Ye. A. Tumanova
Residuality by finite p-groups of HNN-extensions of groups The sufficient condition for the HNN-extension of a finite p-group with central associated subgroups to be residually a finite p-group is obtained.
S. I. Khashin
Three simplifying assumptions for Runge - Kutta methods A new approach to simplifying assumptions in the system of polynomial Butcher's equations used to find the Runge - Kutta methods. Conditions of applicability both classical, and new simplifying assumptions are proved. |
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