D. N. Azarov, D. I. Moldavanskii On supersolvable groups which are conjugacy separable in the class of finite p-groups

It is proved that a supersolvable group is conjugacy separable by finite p-groups if and only if it contains an abelian normal torsion-free subgroups of finite p-index.

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E. P. Baranovskii On the L-partitioning of the space E²⁴ which was obtained with the Leech lattice

The Leech lattice is represented as a centering of Voronoi second perfect lattice. It was obtained the set of the primary elements of L-partitioning of the Leech lattice. It was showed that all L-polytopes of Leech lattice are non-basic.
(The first example of an L-polytope which was non-basic polytope of its lattice was constructed by M. Dutour.)

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A. S. Belov On the lower estimate of the uniform norm of the partial sums of a nonnegative trigonometrical polynomial

A sharp lower estimate of the uniform norm of the partial sums of a nonnegative trigonometrical polynomial in terms of the norm of this polynomial is obtained.

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E. A. Ivanova The conjugacy separability in the class of finite p-groups of free products of two groups

It is proved that any free product with amalgamated subgroups of two finite p-groups is a conjugacy p-separable group if and only if it is a residually finite p-group. With the help of this result some sufficient conditions of conjugacy p-separability of a free product of two groups with amalgamated subgroups are established.

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S. V. Kolesnikov On boundedness of Hankel operator in H^\infty space

Let \Gamma be the circle | z | = 1, \varphi(z) - function, bounded and measurable on \Gamma. In this note we find conditions on \varphi(z), necessary and sufficient for boundedness in the space H^\infty of Hankel operator definited by \varphi.

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N. I. Yatskin The description of vocabulary groups over some finite groups

The construction of Z-vocabulary groups over a finite groups is described. A given group is considered as an alphabet for its Z-vocabulary. A word over this alphabet is considered as trivial if all its "literal powers" are equal to the group unit. Using computer calculations we get some information (exhaustive or partial) about Z-vocabulary groups for some finite groups of a small order.

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