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D. N. Azarov
On groups of finite general rank It is proved that if G is a residually finite group of finite general rank then the automorphism group of G and the split extension of G by a residually finite group are residually finite. These results extend corresponding theorems of Smirnov-Baumslag and Mal'cev on finitely generated groups.
E. P. Baranovskii
Lattices which have a Selling frame consist of only vectors of minimal length A lattice is called z-perfect if one of its Selling frames consist of only vectors of minimal length. In this note it is considered some common propeties of z-perfect lattices.
A. S. Belov
On the conditions for convergence (boundedness) in mean of the partial sums of trigonometric Fourier series A new sufficient conditions in terms of the coefficients of trigonometric Fourier series are obtained for convergence (boundedness) in mean of the partial sums of this series that are best possible in some sense.
E. A. Ivanova
The residual nilpotence of free product of two groups with finite amalgamated subgroups Some conditions for the free product G = (H * K; A = B, \phi) of finitely generated nilpotent groups H and K with finite amalgamated subgroups A and B to be residually nilpotent are established. In particular, it is proved that if the torsion subgroups of groups H and K are finite p-groups then the group G is residually nilpotent if and only if it is residually a finite p-group.
E. A. Ivanova, D. I. Modavanskii
On the conjugacy separability of finitely generated nilpotent groups It is proved that for any non-empty proper subset \pi of the set of all primes a finitely generated nilpotent group is conjugacy separable in the class of finite \pi-groups if and only if the torsion subgroup of it is a finite \pi-group and the quotient group by the torsion subgroup is abelian.
S. V. Kolesnikov
About the unconvergency sets of Taylor series for bounded analitic functions It is proved that for arbitrary subset E of \Gamma = {z: | z | = 1} of null logarithmic capacity and type G\delta on \Gamma there exists bounded analitic function f(z), z \in D, such that E is the set of non-convergence for its Teylor series.
E. D. Loginova
On the finite separability of subgroups of a free product of finitely generated abelian groups with centralized subgroups It is proved that all finitely generated subgroups of an amalgamated free product of two finitely generated abelian groups are finitely separable. This implies the finite separability of all finitely generated subgroups of a free product of finitely generated abelian groups with centralized subgroups.
A. A. Tolstopyatov, S. I. Khashin
Construction of algorithm of an order field about at Boolean compression By the given type of a permutation the number of every concrete permutation is calculated. Conversely, by the given type and the number every concrete permutation is obtained. |
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