Asymptotic existence theorems for frames and group divisible designs

In this paper, we establish an asymptotic existence theorem for group divisible designs of type mn with block sizes in any given set K of integers greater than 1. As consequences, we will prove an asymptotic existence theorem for frames and derive a partial asymptotic existence theorem for resolvable group divisible designs.     

Meromorphic Functions on a Riemann Surface to a Locally Semi-convex Space

In this article, vector-valued holomorphic and meromorphic functions on a Riemann surface to a complete Hausdorff locally semi-convex space are discussed. By introducing the concepts of vector-valued holomorphic and meromorphic differential forms, Cauchy's theorem and the Residue theorem of a vector-valued differential form on a Riemann surface are proved. Using the theory on the operator and the theory of a cohomology of a sheaf, we give a proof of the Mittag-Leffler theorem for vector-valued meromorphic functions on a non-compact Riemann surface to a complete Hausdorff locally semi-convex space.     

一个t—范数下的不分明群问题

本文指出了不分明群中一个重要定理并不完全成立，从而将引出一系列理论问题。     

The majority decision function for trees with 3 leaves

Kenneth May in 1952 proved a classical theorem characterizing simple majority rule for two alternatives. The present paper generalizes May’s theorem to the case of three alternatives, but where the voters’ preference relations are required to be trees with alternatives at the leaves. This paper with title “May’s Theorem for Trees” was presented at the joint DIMACS-LAMSADE workshop on Computer Science and Decision Theory, Université Paris-Dauphine, Paris 27–29 October 2004. It appeared in the proceedings Annales du LAMSADE 3 (2004), 259–266.     

全纯扩充的BHW定理的推广

本文得到关于全纯扩充的BHW定理的一个全新的证明,同时也对BHW定 理做出了更一般的推广,并且给出了推广后的BHW定理的两种不同的证明方法.     

About the Schur Index for Ambivalent Groups

An ambivalent group is a finite group all of whose irreducible characters are real valued. By Brauer–Speiser theorem, if G is an ambivalent group, then the absolute Schur index m _Q (χ) = m(χ) ≤2. In this note we shall prove that this property is true also for the derived subgroups of ambivalent groups. Also we will prove that there is a relation between the number of conjugacy classes of 2-regular cyclic subgroups of an ambivalent group and the irreducible characters with absolute Schur index 1.     

Equivariant resolution of points of indeterminacy

We prove an equivariant form of Hironaka's theorem on elimination of points of indeterminacy. Our argument uses canonical resolution of singularities and an extended version of Sumihiro's equivariant Chow lemma.

     

Structure theorems over polynomial rings

Given a polynomial ring R over a field k and a finite group G, we consider a finitely generated graded RG-module S. We regard S as a kG-module and show that various conditions on S are equivalent, such as only containing finitely many isomorphism classes of indecomposable summands or satisfying a structure theorem in the sense of [D. Karagueuzian, P. Symonds, The module structure of a group action on a polynomial ring: A finiteness theorem, preprint, http://www.ma.umist.ac.uk/pas/preprints].     

Equivariant Gysin maps and pulling back fixed points

We develop a new approach to the pulling back fixed points theorem of W. Browder and use it in order to prove various generalizations of this result.

     

A new approach to Matsumoto's theorem

We give a proof of Matsumoto's theorem on K ₂ of a field using techniques from homological algebra. By considering a complex associated to the action of GL(2, F) on P ₁(F) (F a field), we derive the Matsumoto presentation for H ₀ (F ^., H ₂(SL(2, F))) and, by considering the action of GL(n + 1, F) on P ⁿ (F), we prove the stability part of the theorem; namely, that H ₀(F ^., H ₂(SL(2, F))) is isomorphic to H ₂(SL(F)) = K ₂(F).     

On the fine structure of the polygroup blow-up

We study in detail the blow-up procedure described in [BTW01]. We obtain a structure theorem for coreless polygroups as a double quotient space G//H, and a polygroup chunk theorem. Seeking to remove the arbitrary parameter needed for the blow-up, we find canonical Ø-invariant groupoids analogous to G and H above, and show that contains precisely all the arbitrary choices related to the blow-up. Mathematics Subject Classification (2000): 03C45, 03C60     

An upper bound for the representation dimension of group algebras with elementary abelian Sylow p-subgroups

Abstract

In this article, we present an upper bound on the representation dimension of the group algebra of a group with an elementary abelian Sylow p-subgroup. Specifically, if k is a field of characteristic p and G is a group with elementary abelian Sylow p-subgroup P, we prove that the representation dimension of kG is bounded above by the order of P. Key to proving this theorem is the separable equivalence between the two algebras and some nice properties of Mackey decomposition.     

群体多目标最优化的Lagrange对偶性

本文建立了目标和约束为不对称的群体多目标最优化问题的Lagrange对偶规划，在问题的联合弱有效解意义下，得到群体多目标最优化Lagrange型的弱对偶定理、基本对偶定理、直接对偶定理和逆对偶定理。     

The Primitive Permutation Groups of Degree Less Than 4096

In this article we use the Classification of the Finite Simple Groups, the O'Nan–Scott Theorem, and Aschbacher's theorem to classify the primitive permutation groups of degree less than 4096. The results will be added to the primitive groups databases of GAP and MAGMA.     

Ramification of a finite flat group scheme over a local field

In this paper, we analyze ramification in the sense of Abbes-Saito of a finite flat group scheme over the ring of integers of a complete discrete valuation field of mixed characteristic (0,p). We deduce that its Galois representation depends only on its reduction modulo explicitly computed p-power. We also give a new proof of a theorem of Fontaine on ramification of a finite flat Galois representation, and extend it to the case where the residue field may be imperfect.     

On permutation polytopes

In this paper we lay the foundations for the study of permutation polytopes: the convex hull of a group of permutation matrices.We clarify the relevant notions of equivalence, prove a product theorem, and discuss centrally symmetric permutation polytopes. We provide a number of combinatorial properties of (faces of) permutation polytopes. As an application, we classify ?4-dimensional permutation polytopes and the corresponding permutation groups. Classification results and further examples are made available online.We conclude with several questions suggested by a general finiteness result.     

A short proof of Eilenberg and Moore’s theorem

In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group. This work first appeared as a part of the author’s Ph.D. dissertation [3]     

On[m,P_1~(a_1),P_2~(a_2),…,P_s~(a_s)]Index Type Groups

Ｏｎ［ｍ，Ｐ_１~（ａ_１）,Ｐ_２~（ａ_２）,…,Ｐ_ｓ~（ａ_ｓ）］ＩｎｄｅｘＴｙｐｅＧｒｏｕｐｓＬｉＸｉａｎｈｕａ（黎先华）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＧｕｉｚｈｏｕＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｇｕｉｙａｎｇ，５５０００１）Ａ...     

ASYMPTOTIC PROPERTIES OF ELEMENTS IN GROUP RINGS OF FINITE GROUPS

A relation between algebraic degrees of eigenvalues of an element in the group ring Z G of a finite group G and their multiplicities is obtained. This result can be regarded as a theorem on asymptotic behavior of parameters in group rings of finite groups which is a parallel result of several well known theorems concerning the relationships of parameters in finite groups.     

模糊群的模糊同态

引进模糊群的模糊同态概念，给出模糊同态下子模糊群(正规子模糊群)间的对应关系’建立模糊群的模糊同态基本定理，同时讨论模糊群的若干性质，得到一系列等价条件。