A Primitive Ring Associated to a Burnside 3-Group

Let G be a Burnside 3-group constructed by Gupta–Sidki.The group algebra Z₃[G] has a proper ring-quotient which embedsG and is just-infinite and primitive.     

Burnside定理的推广

本文先证得了定理２．１，在这个基础上，推广了Ｂｕｒｎｓｉｄｅ的两个定理．     

Biset Functors as Module Mackey Functors and its Relation to Derivators

In this article, we will show that the category of biset functors can be regarded as a reflective monoidal subcategory of the category of Mackey functors on the 2-category of finite groupoids. This reflective subcategory is equivalent to the category of modules over the Burnside functor. As a consequence of the reflectivity, we can associate a biset functor to any derivator on the 2-category of finite categories.     

由交换群决定的Near环

本文讨论了加群上保持零元的映射集合对映射的加法和乘法作成的Ｎｅａｒ环，研究了它的理想特点，并构造了几类特殊的左，右理想．     

Characteristic Zero Loop Space Homology of Two-Cones

Given a principal ideal domain R of characteristic zero, containing1/2, and a two-cone X of appropriate connectedness and dimension,we present sufficient algebraic conditions for the Hopf algebraFH(X; R) to be isomorphic with the universal enveloping algebraof an R-free graded Lie algebra; here, F stands for free part(that is, quotient by the R-torsion), H for homology, and forthe Moore loop space functor. 2000 Mathematics Subject Classification55P35, 55P62, 57T05, 17B70, 17B35.     

拟Abelian范畴上函子范畴的局部化

通过拟Abelian范畴的局部类构造出函子范畴的局部类,进一步研究函子范畴的局部化范畴与局部化范畴的函子范畴之间的关系.     

A Strengthening of Resolution of Singularities in Characteristic Zero

Let X be a closed subscheme embedded in a scheme W, smooth overa field k of characteristic zero, and let I (X) be the sheafof ideals defining X. Assume that the set of regular pointsof X is dense in X. We prove that there exists a proper, birationalmorphism, : W_r W, obtained as a composition of monoidal transformations,so that if X_r W_r denotes the strict transform of X W then: (1) the morphism : W_r W is an embedded desingularization ofX (as in Hironaka's Theorem); (2) the total transform of I (X) in factors as a product of an invertible sheaf of ideals L supportedon the exceptional locus, and the sheaf of ideals defining thestrict transform of X (that is, . Thus (2) asserts that we can obtain, in a simple manner, theequations defining the desingularization of X. 2000 MathematicalSubject Classification: 14E15.     

集合范畴上超滤函子的余代数

定义了集合范畴上的超滤函子F_u(-),并研究了相关性质.包括函子F_u(-)在有限集上保拉回,一个集合的子集成为F_u-子余代数的充要条件,以及两个余代数之间的态射是F_u-余代数同态的充要条件,子集成为子余代数的充要条件,最后以拓扑空间作为F_u-余代数的具体实例,研究了拓扑空间的连续映射与超滤函子的余代数同态之间的关系.     

有限交换群的Burnside环的增广理想的连续商群的结构

本文对有限交换群的Burnside环的增广理想的n次幂与n 1次幂之商进行了讨论,完整地给出了这类连续商群的结构.     

TTF Triples in Functor Categories

We characterize the hereditary torsion pairs of finite type in the functor category of a ring R that are associated to tilting torsion pairs in the category of R-modules. Moreover, we determine a condition under which they give rise to TTF triples.     

The Dixmier problem, lamplighters and Burnside groups

J. Dixmier asked in 1950 whether every non-amenable group admits uniformly bounded representations that cannot be unitarised. We provide such representations upon passing to extensions by abelian groups. This gives a new characterisation of amenability. Furthermore, we deduce that certain Burnside groups are non-unitarisable, answering a question raised by G. Pisier.     

The Functor of Order-Preserving Functionals of Finite Degree

It is proved that the space of all order-preserving functionals with finite supports is a compact, and if the supports are one-point sets, then this space is the Stone-Chech compactification of a given Tychonoff space. Bibliography: 4 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 313, 2004, pp. 135–138.     

Irreducible Finitary Lie Algebras over Fields of Characteristic Zero

A Lie subalgebraLof (V) is said to befinitaryif it consists of elements of finite rank. We show that if Char = 0, if dim Vis infinite, and ifLacts irreducibly onV, then the derived algebra ofLis simple.     

Zero Divisor Graph for the Ring of Gaussian Integers Modulo n

This article studies the zero divisor graph for the ring of Gaussian integers modulo n, Γ (? _n [i]). For each positive integer n, the number of vertices, the diameter, the girth and the case when the dominating number is 1 or 2 is found.

Complete characterizations, in terms of n, are given of the cases in which Γ (? _n [i]) is complete, complete bipartite, planar, regular or Eulerian.     

Semistable Reduction in Characteristic Zero for Families of Surfaces and Threefolds

We consider the problem of extending the semistable reduction theorem of [KKMS] from the case of one-parameter families of varieties to families over a base of arbitrary dimension. Following [KKMS], semistable reduction of such families can be reduced to a problem in the combinatorics of polyhedral complexes [AK]. In this paper we solve it in the case when the relative dimension of the morphism is at most three, i.e., for families of surfaces and threefolds. Received March 18, 1998, and in revised form October 7, 1998.     

The Burnside problem on periodic groups and related questions

In a 1959–1975 cycle of papers, P.S. Novikov and S.I. Adian created a new method for studying periodic groups based on the classification of periodic words by means of a complicated simultaneous induction. The method was developed for solving the well-known Burnside problem on periodic groups, but it also enabled the authors to solve a number of other difficult problems of group theory. An extended survey of results contained in the cycle of papers mentioned above and of other significant results obtained after 1975 by Adian and other authors on the basis of the developed theory and its modifications is presented.