Generalized uniform covering maps relative to subgroups

In “Rips complexes and covers in the uniform category” (Brodskiy et al., preprint [4]) the authors define, following James (1990) [5], covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. Conditions for the existence of universal uniform covering maps and generalized uniform covering maps are given. This paper extends these results by investigating the existence of these covering maps relative to subgroups of the uniform fundamental group and the fundamental group of the base space.     

Finite Groups Whose Generalized Hypercenter Contains Some Subgroups of Prime Power Order

A subgroup of a group G is said to be S-quasinormal in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be S-quasinormally embedded in G if every Sylow subgroup of H is a Sylow subgroup of some S-quasinormal subgroup of G. In this article, we investigate the structure of the finite group G under the assumption that certain abelian subgroups of prime power order are S-quasinormally embedded in G and lie in the generlized hypercenter of G.     

Automorphism groups of linear spaces and their parabolic subgroups

Suppose that an almost simple group G acts line transitively on a finite linear space S. Let Gx be a point stabilizer in G and suppose that G has socle T, a simple group of Lie type. In this paper we show that if T∩Gx is a parabolic subgroup of T, then G is flag transitive on S.     

The influence of minimal subgroups on the structure of a finite group

We study the detailed structure of a finite group under the assumption that all minimal subgroups of the generalized Fitting subgroup of some normal subgroup of are well-suited in .

     

On generalized m-S-permutable subgroups of a finite group

In this paper, we give some new conditions under which a normal subgroup E of a finite group G is hypercyclically embedded in G, that is, every chief factor of G below E is cyclic.     

一族Hida广义泛函的构造及其性质

本文证明了当一族可微单参数子群｛g0｝0∈R ∪→GL（E），其生成元T被看成是H稠定算子时是自其轭时，有一族可微单参数子群｛L0｝0∈R∪→GL（（E））∪→Y（E，（E））与此相对应。由此我们可得到一族正广义泛函Φx^θ，其相应的测试是一簇转移概率，特别地，当T＝－I时，它们是一簇Ornstein-Unlenbeck转移概率。     

On s-semipermutable subgroups of finite groups

Suppose that G is a finite group and H is a subgroup of G. We say that H is ssemipermutable in G if HGv = GpH for any Sylow p-subgroup Gp of G with （p, ｜H｜） = 1. We investigate the influence of s-semipermutable subgroups on the structure of finite groups. Some recent results are generalized and unified.     

A function space model approach to the rational evaluation subgroups

Let f : U → X be a map from a connected nilpotent space U to a connected rational space X. The evaluation subgroup G _*(U, X; f), which is a generalization of the Gottlieb group of X, is investigated. The key device for the study is an explicit Sullivan model for the connected component containing f of the function space of maps from U to X, which is derived from the general theory of such a model due to Brown and Szczarba (Trans Am Math Soc 349, 4931–4951, 1997). In particular, we show that non Gottlieb elements are detected by analyzing a Sullivan model for the map f and by looking at non-triviality of higher order Whitehead products in the homotopy group of X. The Gottlieb triviality of a fibration in the sense of Lupton and Smith (The evaluation subgroup of a fibre inclusion, 2006) is also discussed from the function space model point of view. Moreover, we proceed to consideration of the evaluation subgroup of the fundamental group of a nilpotent space. In consequence, the first Gottlieb group of the total space of each S ¹-bundle over the n-dimensional torus is determined explicitly in the non-rational case.      

Generalized Fock spaces and Weyl relations for the Dunkl kernel on the real line

In this paper we study a class of generalized Fock spaces associated with the Dunkl operator. Next we introduce the commutator relations between the Dunkl operator and multiplication operator which leads to a generalized class of Weyl relations for the Dunkl kernel.     

On p-nilpotency of finite groups with some subgroups π-quasinormally embedded

Summary A subgroup H of a group G is said to be π-quasinormal in G if it permutes with every Sylow subgroup of G, and H is said to be π-quasinormally embedded in G if for each prime dividing the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some π-quasinormal subgroups of G. We characterize p-nilpotentcy of finite groups with the assumption that some maximal subgroups, 2-maximal subgroups, minimal subgroups and 2-minimal subgroups are π-quasinormally embedded, respectively.     

Geodesics as products of one-parameter subgroups in compact lie groups and homogeneous spaces

We study the geodesic equation for compact Lie groups G and homogeneous spaces $G/H$, and we prove that the geodesics are orbits of products $\exp (t{X}_1)\cdots \exp (t{X}_N)$ of one-parameter subgroups of G, provided that a simple algebraic condition for the Riemannian metric is satisfied. For the group $SO(3)$, we relate this type of geodesics to the free motion of a symmetric top. Moreover, by using series of Lie subgroups of G, we construct a wealth of metrics having the aforementioned type of geodesics.     

The average number of Sylow subgroups of a finite group

We prove that if the average Sylow number (ignoring the Sylow numbers that are one) of a finite group G is ?7, then G is solvable.     

A free product of finitely generated nilpotent groups amalgamating a cycle that is not subgroup separable

We exhibit a counterexample to a recent assertion concerning the subgroup separability of groups in the title. The example also serves as a simplification of work of Gitik and Rips.

     

Normalizers of subsystem subgroups in finite groups of Lie type

Finite groups of Lie type form the greater part of known finite simple groups. An important class of subgroups of finite groups of Lie type are so-called reductive subgroups of maximal rank. These arise naturally as Levi factors of parabolic groups and as centralizers of semisimple elements, and also as subgroups with maximal tori. Moreover, reductive groups of maximal rank play an important part in inductive studies of subgroup structure of finite groups of Lie type. Yet a number of vital questions dealing in the internal structure of such subgroups are still not settled. In particular, we know which quasisimple groups may appear as central multipliers in the semisimple part of any reductive group of maximal rank, but we do not know how normalizers of those quasisimple groups are structured. The present paper is devoted to tackling this problem. Supported by RFBR (grant No. 05-01-00797) and by SB RAS (Young Researchers Support grant No. 29 and Integration project No. 2006.1.2). __________ Translated from Algebra i Logika, Vol. 47, No. 1, pp. 3–30, January–February, 2008.     

Generalized solutions to a linear discontinuous differential equation

In this paper we construct generalized solutions (weak solutions) to a linear discontinuous differential equation which appears as mathematical model in mechanics and for which usual methods are not quite adequate. The result is applied to the equation of an elastic beam on a Winkler type of foundation.     

Generalized Cauchy functional equation and characterizations of inner product spaces

Summary Using a generalized Cauchy functional equation we show that some well-known characterizations of inner product spaces, such as those of Jordan—von Neumann, Johnson, and Rassias, can be proved without use of the triangle inequality.     

Normal subgroups of

We classify the normal subgroups of of index less than 960; they are all congruence subgroups.