t. Some properties of abnormal subgroups in generalized soluble groups are considered. In particular, the transitivity of abnormality in metahypercentral groups is proven. Also it is proven that a subgroup H of a radical ...

Let X be a set of cardinality k, F be a family of subsets of X. We say that a cardinal λ,λ<k, is a color-detector of the hypergraph H=(X,F) if card χ(X)≤λ for every coloring χ:X→k such that card χ(F)≤λ for every F∈F. ...

Let A = (aij ) be an integral matrix. We say that A is (0, 1, 2)-matrix if aij ∈ {0, 1, 2}. There exists the Gorenstein (0, 1, 2)-matrix for any permutation σ on the set {1, . . . , n} without fixed elements. For every ...

We describe a new algebraic-combinatorial method of public key encryption with a certain similarity to the well known Imai-Matsumoto. We use the general idea to treat vertices of a linguistic graph (see [21] and further ...

In this paper we consider the problem on classifying the representations of a pair of posets with involution. We prove that if one of these is a chain of length at least 4 with trivial involution and the other is with ...

This is an expository paper on some realizations of affine Lie algebras and their representations in terms of differential operators. In particular we recall the classical construction of Wakimoto modules and its recent ...

We define a wreath product of a Lie algebra L with the one-dimensional Lie algebra L1 over Fp and determine some properties of this wreath product. We prove that the Lie algebra associated with the Sylow p-subgroup of ...