A conjecture on bipartite graphical regular representations

In this paper we are concerned with the classification of the finite groups admitting a bipartite DRR and a bipartite GRR.First, we find a natural obstruction that prevents a finite group from admitting a bipartite GRR. Then we give a complete classification of the finite groups satisfying this natural obstruction and hence not admitting a bipartite GRR. Based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite GRR.Next, we prove the existence of bipartite DRRs for most of the finite groups not admitting a bipartite GRR found in this paper. Actually, we prove a much stronger result: we give an asymptotic enumeration of the bipartite DRRs over these groups. Again, based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite DRR.     

Nichols Algebras of Unidentified Diagonal Type

Abstract

The groups having exactly one normalizer are well-known. They are the Dedekind groups. All finite groups having exactly two normalizers were classified by M. D. Pérez-Ramos and, in a recent paper, S. Camp-Mora generalized that result to locally finite groups. In this paper, we will characterize arbitrary groups with a finite number of normalizers and we will investigate the properties of arbitrary groups with two, three and four normalizers.     

Centraliser Dimension of Partially Commutative Groups

In a previous paper (Centraliser Dimension and Universal Classes of Groups), we investigated the centraliser dimension of groups. In the current paper we study properties of centraliser dimension for the class of free partially commutative groups and, as a corollary, we obtain an efficient algorithm for computation of centraliser dimension in these groups.Ilya V. Kazachkov, Vladimir N. Remeslennikov: Supported by RFFI grant N05-01-00057-a     

带作用的群系的临界结构

在本文中，我们讨论了带作用群的群系的临界结构，给出了处理允许某些作用群的群的问题的一般方法，作为应用，我们特别给出了关于幂零群及ｐ－幂零群的一些结果。     

三维初等群的分类及特殊椭圆子群的表示

本文利用 ｄｉｆｆｏｒｄ矩阵，得出三维初等群的分类，此外，并对特殊椭圆群进行表示．     

p-幂零群和p-闭群的若干充分条件

交换子群的中心化子和正规化子对有限群的结构有很强的控制作用,本文主要通过考虑某些交换子群的中心化子一致于正规化子,得到了p-幂零群和p-闭群的若干充分条件.     

Some computations of stable twisted homology for mapping class groups

Abstract

In this paper, we deal with stable homology computations with twisted coefficients for mapping class groups of surfaces and of 3-manifolds, automorphism groups of free groups with boundaries and automorphism groups of certain right-angled Artin groups. On the one hand, the computations are led using semidirect product structures arising naturally from these groups. On the other hand, we compute the stable homology with twisted coefficients by FI-modules. This notably uses a decomposition result of the stable homology with twisted coefficients for pre-braided monoidal categories proved in this paper.

Communicated by Jason P. Bell     

Z2上平延群的有理不变量

本文研究了Z2上平延群的有理不变量.利用矩阵的方法,获得了平延群的一组超越基.     

Algebraic K-theory of generalized free products and functors Nil

In this paper, we extend Waldhausen's results on algebraic K-theory of generalized free products in a more general setting and we give some properties of the Nil functors. As a consequence, we get new groups with trivial Whitehead groups.     

On Direct Product of HX Groups

ＯｎＤｉｒｅｃｔＰｒｏｄｕｃｔｏｆＨＸＧｒｏｕｐｓＭｉＨｏｎｇｈａｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＰｈｙｓｉｃｓ，ＨｅｂｅｉＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ）ＺｅｎｇＷｅｎｙｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍ...     

Fuzzy幂群与Fuzzy商群的相互关系

In this paper,we extend the concept of fuzzy quotient groups.The structures of fuzzy power groups and fuzzy quotient groups are discussed.The relationship between fuzzy power groups and fuzzy quotient groups are considered.     

Graphical complexity of products of permutation groups

In this paper we study representations of permutation groups as automorphism groups of colored graphs and supergraphs. In particular, we consider how such representations for various products of permutation groups can be obtained from representations of factors and how the degree of complexity increases in such constructions.     

Fuzzy群的半格

引入 Fuzzy群的半格的概念 ,并讨论它们的一些代数性质。同时利用 Fuzzy理想对 Fuzzy群的半格作了一些等价刻画。     

半次覆盖远离子群和有限群的可解性

本文定义了有限群的半次覆盖远离子群概念,研究了半次覆盖远离子群和有限群的可解性问题.利用某些半次覆盖远离子群刻划了有限群的可解性,得到了若所有的sylow子群(或极大子群)半次覆盖远离则群可解,推广了文献[6]中的结果.     

Abelian subgroup separability of certain generalized free products of free or finitely generated nilpotent groups

In this paper we prove that certain generalized free products of abelian subgroup separable groups, amalgamating an infinite cyclic subgroup, are abelian subgroup separable. Applying this, we derive that tree products of free groups or finitely generated nilpotent groups, amalgamating infinite cyclic subgroups, are abelian subgroup separable.     

Spinor Frenet Equations in Three Dimensional Lie Groups

In this paper, we study spinor Frenet equations in three dimensional Lie groups with a bi-invariant metric. Also, we obtain spinor Frenet equations for some special cases of three dimensional Lie groups.     

L-Fuzzy子格群的若干刻画

在L是完全分配格时，讨论L-Fuzzy子格群的一些特征性质。特别地，借助L—Fuzzy集的几种水平截集给出它的若干刻画。最后给出这些刻画的一个应用。     

Isometric actions on the four dimensional Minkowski spacetime

In this paper we give representations of all connected Lie groups acting isometrically on the four dimensional Minkowski spacetime, up to conjugacy within the full isometry group of the space. For each obtained group, we study its induced orbits. Then we classify the Lie groups up to orbit equivalence.     

Uncertainty principles for locally compact quantum groups

In this paper, we prove the Donoho–Stark uncertainty principle for locally compact quantum groups and characterize the minimizer which are bi-shifts of group-like projections. We also prove the Hirschman–Beckner uncertainty principle for compact quantum groups and discrete quantum groups. Furthermore, we show Hardy's uncertainty principle for locally compact quantum groups in terms of bi-shifts of group-like projections.