典型群PSU（3，q2）与2—（v,k,1）设计

讨论自同构群是酉群PSU（3,q2)(q=2^l)的区－本原的2-(v,k,1)设计,首先证明了它必是点－本原的,然后确定了这种类型的设计,即它只能为2－（q3 1,q 1,1)设计。     

A Family of Non-quasiprimitive Graphs Constructed From PSU3（q） Where q Is Odd

Let Г be a simple connected graph and let G be a group of automorphisms of Г. Г is said to be （G, 2）-arc transitive if G is transitive on the 2-arcs of Г. It has been shown that there exists a family of non-quasiprimitive （PSU3（q）, 2）-arc transitive graphs where q = 2^3m with m an odd integer. In this paper we investigate the case where q is an odd prime power.     

Constructions of （q,K, λ, t,Q） almost difference families

The concept of a （q, k, λ, t） almost dltterence tamlly （ADF） nas oeen introduced and studied by C. Ding and J. Yin as a useful generalization of the concept of an almost difference set. In this paper, we consider, more generally, （q, K,λ, t, Q）-ADFs, where K = {k1, k2,.…, kr} is a set of positive integers and Q = （q1,q2,... ,qr） is a given block-size distribution sequence. A necessary condition for the existence of a （q, K, λ, t, Q）-ADF is given, and several infinite classes of （q, K, A, t, Q）-ADFs are constructed.     

COSET DIAGRAMS FOR A HOMOMORPHIC IMAGE OF △（3, 3, k）

Let q be a prime power. By PL（Fq） the authors mean a projective line over the finite field Fq with the additional point ∞. In this article, the authors parametrize the conjugacy classes of nondegenerate homomorphisms which represent actions of △（3, 3, k） = （u, v： u^3 = v^3 = （uv）^k = 1〉on PL（Fq）, where q ≡ ±1（modk）. Also, for various values of k, they find the conditions for the existence of coset diagrams depicting the permutation actions of △（3, 3, k） on PL（Fq）. The conditions are polynomials with integer coefficients and the diagrams are such that every vertex in them is fixed by （u^-v^-）^k. In this way, they get △（3, 3, k） as permutation groups on PL（Fq）.     

^2F4（q2）与2-（v，k，3）对称设计

本文要证明不存在一个非平凡2-（v，k，3）对称设计，它的旗传递自同构群的基柱是^2F4（q2）     

Some Aspects of Lw1^r （G）∩ L（p,q, w2dμ）（G）

Let G be a locally compact Abelian group with Haar measure. The authors discuss some basic properties of Lw1^r （G）∩ L（p, q, w2dμ）（G） spaces. Then the necessary conditions for compact embeddings of the spaces Lw1^r （R^d）∩ L（p, q, w2dμ）（R^d） are showed.     

A Class of Finite-Dimensional Representations of U_q（sl_2）

In order to study a class of finite-dimensional representations of Uq（sl2）, we deal with the quotient algebra Uq （m, n, b） of quantum group Uq（sl2） with relations Kr=1, Emr=b, Fnr=0 in this paper, where q is a root of unity. The algebra Uq（m, n, b） is decomposed into a direct sum of indecomposable （left） ideals. The structures of indecomposable projective representations and their blocks are determined.     

^3D4（q）群与射影平面

本文证明若^3D4（q）△G≤Aut（^3D4（q）），这里q是素数方幂，则G不能点传递作用在一个射影平面上.     

区传递的$2-(v, k, 1)$ 设计与单群$E_6(q)$

This article is a contribution to the study of block-transitive automorphism groups of 2-（v,k,1） block designs. Let D be a 2-（v,k,1） design admitting a block-transitive, pointprimitive but not flag-transitive automorphism group G. Let kr = （k,v-1） and q = pf for prime p. In this paper we prove that if G and D are as above and q （3（krk-kr ＋ 1）f）1/3, then G does not admit a simple group E6（q） as its socle.     

The Order of Hypersubstitutions of Type （2, 2）

Hypersubstitutions are mappings which map operation symbols to terms of the corresponding arities. They were introduced as a way of making precise the concept of a hyperidentity and generalizations to M-hyperidentities. A variety in which every identity is satisfied as a hyperidentity is called solid. If every identity is an M-hyperidentity for a subset M of the set of all hypersubstitutions, the variety is called M-solid. There is a Galois connection between monoids of hypersubstitutions and sublattices of the lattice of all varieties of algebras of a given type. Therefore, it is interesting and useful to know how semigroup or monoid properties of monoids of hypersubstitutions transfer under this Galois connection to properties of the corresponding lattices of M-solid varieties. In this paper, we study the order of each hypersubstitution of type （2, 2）, i.e., the order of the cyclic subsemigroup generated by that hypersubstitution of the monoid of all hypersubstitutions of type （2, 2）. The main result is that the order is 1, 2, 3, 4 or infinite.     

Tetravalent Edge-transitive Cayley Graphs of PGL （2, p）

t Let F = Cay（G, S）, R（G） be the right regular representation of G. The graph Г is called normal with respect to G, if R（G） is normal in the full automorphism group Aut（F） of F. Г is called a bi-normal with respect to G if R（G） is not normal in Aut（Г）, but R（G） contains a subgroup of index 2 which is normal in Aut（F）. In this paper, we prove that connected tetravalent edge-transitive Cayley graphs on PGL（2,p） are either normal or bi-normal when p ≠ 11 is a prime.     

On Pseudo-Holomorphic Curves from Two-Spheres into a Complex Grassmannian G（2, 5）

Let s ： S2 → G（2, 5） be a linearly full totally unramified pseudo-holomorphic curve with constant Gaussian curvature K in a complex Grassmann manifold G（2, 5）. It is prove that K is either 1 4 1 or 4/5 if s is non-±holomorphic. Furthermore, K = 1/3 if and only if s is totally real. We also prove that the Gaussian curvature K is either 1 or -4/3 if s is a non-degenerate holomorphic curve under some conditions.     

L7（3）与GL7（3）的OD-刻画

对于任意一个有限群G,令π（G）表示由它的阶的所有素因子构成的集合.构建一种与之相关的简单图,称之为素图,记作Γ（G）.该图的顶点集合是π（G）,图中两顶点p,g相连（记作p～q）的充要条件是群G恰有pq阶元.设π（G）={P₁,p2,…,p_x}.对于任意给定的p∈π（G）,令deg（p）:=|{q∈π（G）|在素图Γ（G）中,p～q}|,并称之为顶点p的度数.同时,定义D（G）:=（deg（p₁）,deg（p₂）,…,deg（p_s））,其中p₁2<…相似文献   

区传递的2-（v，k，1）设计与李型单群E8（q）

分类自同构群的基柱为李型单群E8（q）的区传递2-（v，k，1）设计，得到如下定理：设D为一个2-（v，k，1）设计，G≤Aut（D）是区传递、点本原但非旗传递的．若q〉24√（krk-kr＋1）f（这里kr=（k，v-1），q=p^f，p是素数，f是正整数），则Soc（G）≌／E8（q）．     

Characterizability of the Group ^2Dp（3） by its Order Components,Where p ≥ 5 is a Prime Number Not of the Form 2^m ＋ 1

The author will prove that the group ^2Dp（3） can be uniquely determined by its order components, where p ≠ 2^m ＋ 1 is a prime number, p ≥ 5. More precisely, if OC（G） denotes the set of order components of G, we will prove OC（G） = OC（^2Dp（3）） if and only if G is isomorphic to ^2Dp（3）. A main consequence of our result is the validity of Thompson＇s conjecture for the groups under consideration.     

Gauss Sum of Index 4： （2） Non-cyclic Case

Assume that m ≥ 2, p is a prime number, （m,p（p - 1）） = 1,-1 not belong to 〈p〉 belong to （Z/mZ）^＊ and [（Z/mZ）^＊：〈p〉]=4.In this paper, we calculate the value of Gauss sum G（X）=∑x∈F^＊x（x）ζp^T（x） over Fq,where q=p^f,f=φ（m）/4,x is a multiplicative character of Fq and T is the trace map from Fq to Fp.Under our assumptions,G（x） belongs to the decomposition field K of p in Q（ζm） and K is an imaginary quartic abelian unmber field.When the Galois group Gal（K/Q） is cyclic,we have studied this cyclic case in anotyer paper：＂Gauss sums of index four：（1）cyclic case＂（accepted by Acta Mathematica Sinica,2003）.In this paper we deal with the non-cyclic case.     

SUZUKI GROUPS Sz（q） AND 2-（v,k, 1） BLOCK DESIGNS

It is proved that if D be a 2-(v,k,1) design with G≤Aut D block primitive then G does not have a Suzuki group Sz(q) as the socle.     

Maximum two-dimensional （u × v, 4, 1, 3）-OOCs

Let Ф（u ×v, k, Aa, Ac） be the largest possible number of codewords among all two- dimensional （u ×v, k, λa, λc） optical orthogonal codes. A 2-D （u× v, k, λa, λ）-OOC with Ф（u× v, k, λa, λc） codewords is said to be maximum. In this paper, the number of codewords of a maximum 2-D （u × v, 4, 1, 3）-OOC has been determined.     

A RECOGNITION OF SIMPLE GROUPS PSL（3, q） BY THEIR ELEMENT ORDERS

For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.     

搜索区传递2-（q，4，1）设计

对于区传递但非旗传递的可解2-（q，4，1）设计，Camina指出，当q=13，37，61，109，157，181时有具体的例子，但是否有更多的q产生具体例子有待研究。主要结果：设q是素数幂且q=13（mod24），则对于每个q〈2000，总存在区传递但非旗传递的2-（q，4，1）设计。