Generalized factorized groups with dispersible subgroups

We generalize the well-known nition of complementability of subgroups. We describe the structure of nondispersible generalized factorized groups all subgroups of which are dispersible. Ukrainian Pedagogical University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 8, pp. 1025–1031, August. 1997.     

Groups in which the commutant is generated by invariant cyclic subgroups

We study groups in which the commutant is generated by invariant cyclic subgroups. Existence of a hypercentral coradical in a periodic group is proved and a completability criterion is derived for some subgroups of the coradical.Kiev Polytechnical Institute. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 74, pp. 85–88, 1992;     

On the theory of groups with generalized minimality condition for closed subgroups

We prove that a topological Abelian locally compact group with generalized minimality condition for closed subgroups is a group of one of the following types: 1) a group with minimality condition for closed subgroups, 2) an additive group of theJ _p -ring of integerp-adic numbers, 3) an additive groupR _p of the field ofp-adic numbers (p is a prime number). Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 3, pp. 398–409, March, 1999.     

ZD-coradical of aKI-group

We consider existence and completability of the ZD-coradical of a group in which all the subgroups of the commutant are invariant.Kiev Polytechnical Institute. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 120–124, 1991.     

Decompositions of direct products of groups

We propose a new method for the decomposition of direct products of groups into U subsets. By using this method, we prove the following generalization of the Comfort-van Mill theorem: An arbitrary nondiscrete topological Abelian group with a finite number of second-order elements can be decomposed into a countable number of dense subsets. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 10, pp. 1385–1395, October, 1997.     

Groups satisfying the minimality condition for non-almost-layer-finite subgroups

The following theorem characterizing the class of almost layer-finite groups in the class of periodic groups without involutions is proved: Each conjugate-biprimitively finite group without involutions that satisfies the minimality condition for non-almost-layer-finite subgroups is almost layerfinite.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 1002–1008, July–August, 1991.     

Investigation of the mechanical properties and internal stress field of directionally reinforced materials in transverse tension

The dependence of the transverse Young's modulus and Poisson's ration on the reinforcement ratio, type of structure, and internal fiber radius has been investigated. The microstress field in the structure of a composite in transverse tension is analyzed. Simple approximate expressions, which can be used to determine the corresponding mechanical characteristics without analyzing the state of stress, are obtained from the exact equations. A medium reinforced with doubly periodic groups is taken as a model. The exact solutions of the problem are obtained by means of elliptic functions.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 5, pp. 812–817, September–October, 1970.     

On the Howson property of HNN-extensions with abelian base group and amalgamated free products of abelian groups

We give necessary and sufficient conditions under which an HNN-extension with abelian base group or an amalgamated free product of abelian groups is a Howson group (that is the intersection of any two finitely generated subgroups is finitely generated). We describe HNN-extensions and amalgamated free products which are Howson groups without satisfying the Burns–Cohen statements.     

Interpolation of entire functions with infinitely many nodes

A method is described for the construction of an interpolating entire function for any countable set of interpolation nodes without condensation points in a finite domain, given the values of the function and its derivative at the interpolation nodes.Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 26–34, 1991.     

The integral Novikov conjectures for S-arithmetic groups I

We prove the integral Novikov conjecture for torsion free S-arithmetic subgroups Γ of linear reductive algebraic groups G of rank 0 over a global field k. They form a natural class of groups and are in general not discrete subgroups of Lie groups with finitely many connected components. Since many natural S-arithmetic subgroups contain torsion elements, we also prove a generalized integral Novikov conjecture for S-arithmetic subgroups of such algebraic groups, which contain torsion elements. These S-arithmetic subgroups also provide a natural class of groups with cofinite universal spaces for proper actions. Partially Supported by NSF grants DMS 0405884 and 0604878.     

Restrictions of modules over classical groups to subgroups of type <Emphasis Type="Italic">A</Emphasis><Subscript>2</Subscript> in characteristic 2

Restrictions of irreducible modules over classical groups to subsystem subgroups of type A ₂ in characteristic 2 are studied. The composition factors (without their multiplicities) for restrictions of such modules with 2-restricted highest weights are found. Bibliography: 7 titles.     

Parabolic subgroups in FC-type Artin groups

Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called the complex of parabolic subgroups, to FC-type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is δ-hyperbolic.     

A joinings classification and a special case of Raghunathan’s conjecture in positive characteristic (with an appendix by Kevin Wortman)

We prove the classification of joinings for maximal horospherical subgroups acting on homogeneous spaces without any restriction on the characteristic. Using the linearization technique, we deduce a special case of Raghunathan’s orbit closure conjecture. In the appendix, quasi-isometries of higher rank lattices in semisimple algebraic groups over fields of positive characteristic are characterized.     

On Influence of Contranormal Subgroups on the Structure of Infinite Groups

Following Rose, a subgroup H of a group G is called contranormal, if G = H ^G . In certain sense, contranormal subgroups are antipodes to subnormal subgroups. It is well known that a finite group is nilpotent if and only if it has no proper contranormal subgroups. However, for the infinite groups this criterion is not valid. There are examples of non-nilpotent infinite groups whose subgroups are subnormal; in paricular, these groups have no contranormal subgroups. Nevertheless, for some classes of infinite groups, the absence of contranormal subgroups implies the nilpotency of the group. The current article is devoted to the search of such classes. Some new criteria of nilpotency in certain classes of infinite groups have been established.     

Compressing strongly connected subgroups in social networks: An entropy-based approach

To detect and study cohesive subgroups of actors is a main objective in social network analysis. What are the respective relations inside such groups and what separates them from the outside. Entropy-based analysis of network structures is an up-and-coming approach. It turns out to be a powerful instrument to detect certain forms of cohesive subgroups and to compress them to superactors without loss of information about their embeddedness in the net: Compressing strongly connected subgroups leaves the whole net’s and the (super-)actors’ information theoretical indices unchanged; i.e., such compression is information-invariant. The actual article relates on the reduction of networks with hundreds of actors. All entropy-based calculations are realized in an expert system shell.     

Groups with finitely many derived subgroups of non-normal subgroups

A group is called metahamiltonian if all its non-abelian subgroups are normal; it is known that locally soluble metahamiltonian groups have finite derived subgroup. This result is generalized here, by proving that every locally graded group with finitely many derived subgroups of non-normal subgroups has finite derived subgroup. Moreover, locally graded groups having only finitely many derived subgroups of infinite non-normal subgroups are completely described. Received: 25 April 2005     

Almost isomorphism of Abelian groups and determinability of Abelian groups by their subgroups

An Abelian group A is called correct if for any Abelian group B isomorphisms A ≅ B′ and B ≅ A′, where A′ and B′ are subgroups of the groups A and B, respectively, imply the isomorphism A ≅ B. We say that a group A is determined by its subgroups (its proper subgroups) if for any group B the existence of a bijection between the sets of all subgroups (all proper subgroups) of groups A and B such that corresponding subgroups are isomorphic implies A ≅ B. In this paper, connections between the correctness of Abelian groups and their determinability by their subgroups (their proper subgroups) are established. Certain criteria of determinability of direct sums of cyclic groups by their subgroups and their proper subgroups, as well as a criterion of correctness of such groups, are obtained. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 21–36, 2003.     

Normal structure of the jonquere group over a field of characteristic zero

The lattice of normal divisors of the Jonquere group over a field of characteristic zero is described. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 692–698, June, 1994.