无限箭图的同调群

对任意箭图Q,我们研究路代数A=kQ的Hochschild同调群H_n(A)和同调群Tor_n^Ae(A,A),其中A^e是代数A的包络代数。在本文中,我们具体地给出了各次同调群和Hochschild同调群。     

Isomorfismi tra le strutture subnormali dei gruppi

Summary In this paper order-isomorphisms between subnormal structures of subsoluble groups are considered, and the images of generalized nilpotent groups in such isomorphisms are studied. A result of Pazderski about the Fitting subgroup of finite soluble groups is also extended to the upper Baer series of subsoluble groups, and an extension to infinite groups of a theorem of Heineken about isomorphisms between lattices of subnormal subgroups of finite groups is given.

---

---

Lavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R.     

On groups whose subgroups are closed in the profinite topology

A group is called extended residually finite (ERF) if every subgroup is closed in the profinite topology. The ERF-property is studied for nilpotent groups, soluble groups, locally finite groups and FC-groups. A complete characterization is given of FC-groups which are ERF.     

Actions of Picture Groups on CAT(0) Cubical Complexes

A class of groups, called picture groups, is defined. Richard Thompsons groups F, T, and V are all picture groups. Each picture group is shown to act properly and isometrically on a CAT(0) cubical complex. In particular, all picture groups are a-T-menable.Mathematics Subject Classifications (2000). 20F65, 43A15.     

On varieties of n-solvable groups

A new and shorter proof is given for the fundamental theorem of Kaluzhnin's recent note [1]: A variety of n-Abelian groups is the sum of a variety of Abelian groups and the respective Burnside varieties of groups of exponent n and 1–n. This theorem is extended to varieties of n-solvable groups.Translated from Matematicheskie Zametki, Vol. 4, No. 6, pp. 629–634, December, 1968.     

On semidirect products and wreath products of partially ordered groups

The notions of Cartesian and semidirect products for partially ordered groups are considered. A series of results on those products of AO \mathcal{A}\mathcal{O} -groups and interpolation groups is obtained. Some results concerning wreath products of directed groups are obtained.     

A note on groups and permutation-partition pairs

ANNALI DELL'UNIVERSITA' DI FERRARA - A link between permutation-partition pairs and finite presentations of groups, leading to a graph-theoretical representation of groups, is presented. A...     

On Characteristic Polynomials of Formal Groups over Finite Fields

Generalizing the results of Serre, Hill and Koch, we give some classification theorems of higher dimensional simple formal groups over finite fields. A relation between endomorphism rings of formal groups over ?_p and characteristic polynomials of their reductions mod p is studied. A condition of existence of formal groups over ?_p with complex multiplication is given. Some formal groups over ?_p are also constructed.     

New proofs of Plünnecke-type estimates for product sets in groups

We present a new method to bound the cardinality of product sets in groups and give three applications. A new and unexpectedly short proof of the Plünnecke-Ruzsa sumset inequalities for commutative groups. A new proof of a theorem of Tao on triple products, which generalises these inequalities when no assumption on commutativity is made. A further generalisation of the Plünnecke-Ruzsa inequalities in general groups.     

Regular symmetric groups of boolean functions

We show that with the exception of four known cases: C₃, C₄, C₅, and , all regular permutation groups can be represented as symmetric groups of boolean functions. This solves the problem posed by A. Kisielewicz in the paper [A. Kisielewicz, Symmetry groups of boolean functions and constructions of permutation groups, J. Algebra 199 (1998) 379-403]. A slight extension of our proof yields the same result for semiregular groups.     

Characterization of generalized Chernikov groups among groups with involutions

The class of generalized Chernikov groups is characterized, i.e., the class of periodic locally solvable groups with the primary ascending chain condition. The name of the class is related to the fact that the structure of such groups is close to that of Chernikov groups. Namely, a Chernikov group is defined as a finite extension of a direct product of finitely many quasi-cyclic groups, and a generalized Chernikov group is a layer-finite extension of a direct productA of quasi-cyclicp-groups with finitely many factors for each primep such that each of its elements does not commute elementwise with only finitely many Sylow subgroups ofA. A theorem that characterizes the generalized Chernikov groups in the class of groups with involution is proved. Translated fromMatematicheskie Zametki, Vol. 62, No 4, pp. 577–587, October, 1997. Translated by A. I. Shtern     

On prime radicals and wreath products of partially ordered groups

The notion of a wreath product for partially ordered groups is considered. A series of results on semidirect products of $ \mathcal{A}\mathcal{O} $ -groups and interpolation groups is obtained. Some results are obtained concerning prime radicals of directed groups.     

Asymptotic properties of groups acting on complexes

We examine asymptotic dimension and property A for groups acting on complexes. In particular, we prove that the fundamental group of a finite, developable complex of groups will have finite asymptotic dimension provided the geometric realization of the development has finite asymptotic dimension and the vertex groups are finitely generated and have finite asymptotic dimension. We also prove that property A is preserved by this construction provided the geometric realization of the development has finite asymptotic dimension and the vertex groups all have property A. These results naturally extend the corresponding results on preservation of these large-scale properties for fundamental groups of graphs of groups. We also use an example to show that the requirement that the development have finite asymptotic dimension cannot be relaxed.

     

Completeness in Zariski groups

Zariski groups are ℵ₀-stable groups with an axiomatically given Zariski topology and thus abstract generalizations of algebraic groups. A large part of algebraic geometry can be developed for Zariski groups. As a main result, any simple smooth Zariski group interprets an algebraically closed field, hence is almost an algebraic group over an algebraically closed field.     

Endomorphism Rings of Faithfully Flat Abelian Groups

We discuss faithfully flat abelian groups in conjunction with the following: A class C of abelian groups with full A-socle is A-balanced closed if it is closed with respect to finite direct sums and subgroups with full A-socle, ker ? ε C for all ? ε Horn (G, H) and G, H ε C, and A is projective with respect to all exact sequences of elements of C. A self-small group A admits an A-balanced closed class C which contains ⊕_IA for all index-sets I exactly if it is faithfully flat as an E(A)-module. We show that Corner's as well as Dugas' and Göbel's realization theorems yield abelian groups that are faithfully flat as E(A)-modules. Several applications of these results are given, some of which yield an answer to part a of Fuchs' Problem 84 and a partial respond to part c of the same problem.     

Whitehead groups and the Bass conjecture

This paper will be concerned with proving that certain Whitehead groups of torsion-free elementary amenable groups are torsion groups and related results, and then applying these results to the Bass conjecture. In particular we shall establish the strong Bass conjecture for an arbitrary elementary amenable group. Mathematics Subject Classification (2000): 19A31, 19B28, 16A27, 16E20, 20C07The first author was supported in part by the National Science Foundation     

Geometry of PDE's. IV: Navier-Stokes equation and integral bordism groups

Following our previous results on this subject [R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(I): Webs on PDE's and integral bordism groups. The general theory, Adv. Math. Sci. Appl. 17 (2007) 239-266; R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's, Adv. Math. Sci. Appl. 17 (2007) 267-285; A. Prástaro, Geometry of PDE's and Mechanics, World Scientific, Singapore, 1996; A. Prástaro, Quantum and integral (co)bordism in partial differential equations, Acta Appl. Math. (5) (3) (1998) 243-302; A. Prástaro, (Co)bordism groups in PDE's, Acta Appl. Math. 59 (2) (1999) 111-201; A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing Co, Singapore, 2004, 500 pp.; A. Prástaro, Geometry of PDE's. I: Integral bordism groups in PDE's, J. Math. Anal. Appl. 319 (2006) 547-566; A. Prástaro, Geometry of PDE's. II: Variational PDE's and integral bordism groups, J. Math. Anal. Appl. 321 (2006) 930-948; A. Prástaro, Th.M. Rassias, Ulam stability in geometry of PDE's, Nonlinear Funct. Anal. Appl. 8 (2) (2003) 259-278; I. Stakgold, Boundary Value Problems of Mathematical Physics, I, The MacMillan Company, New York, 1967; I. Stakgold, Boundary Value Problems of Mathematical Physics, II, Collier-MacMillan, Canada, Ltd, Toronto, Ontario, 1968], integral bordism groups of the Navier-Stokes equation are calculated for smooth, singular and weak solutions, respectively. Then a characterization of global solutions is made on this ground. Enough conditions to assure existence of global smooth solutions are given and related to nullity of integral characteristic numbers of the boundaries. Stability of global solutions are related to some characteristic numbers of the space-like Cauchy data. Global solutions of variational problems constrained by (NS) are classified by means of suitable integral bordism groups too.     

Characterization of groups with generalized chernikov periodic part

A characterization of groups with generalized Chernikov periodic part is obtained first in the class of groups without elements of order 2 and then without this restriction. Two author’s theorems for periodic groups are generalized to mixed groups. Translated fromMatematicheskie Zametki, Vol. 67, No. 2, pp. 270–275, February, 2000.     

The existence of inner invariant means on L(G)

The purpose of this paper is to generalize the concepts of amenability for locally compact groups and inner amenability for discrete groups by considering the existence of inner invariant means. Based on this generalization, locally compact groups can be classified as so called [IA] groups or non-[IA] groups. A number of equivalent conditions characterizing [IA] groups are given. Also the possibility of inner invariant extension of the Dirac measure δ_e is discussed.