主理想环上子群Gr在线性群中的扩群

Suppose R is a principal ideal ring,R~* is a multiplicative group which is composed of all reversible elements in R,and M_n(R),GL(n,R),SL(n,R) are denoted by, M_n(R)={A=(a_(ij))_(n×n)|a_(ij)∈R,i,j=1,2,…,n},GL(n,R) = {g|g∈M_n(R),detg∈R~*},SL(n,R) = {g∈GL(n,R)|det g=1},SL(n,R)≤G≤GL(n,R)(n≥3),respectively, then basing on these facts,this paper mainly focus on discussing all extended groups of G_r={(AB OD)∈G|A∈GL(r,R),(1≤r相似文献   

一类域上的线性变换环的群结构

In this paper, we introduce a practical method for obtaining the structure of the group of units for the ring of linear transformations of a vector space over an arbitrary field, and we give a further generalization of the result in [3].     

The Sylow p-Subgroups of a Limiting (Stable) Linear Group over an Algebraically Closed Field

In Math. Zh. 36(3) (1963), 240–246, we considered the classification of Sylow p-subgroups of a countable (finitary) symmetric group. Later, we extended this classification to Sylow p-subgroups of a limiting (stable) linear group over a finite field GF(q) with char(GF(q)) p. In this paper, the classification of the Sylow p-subgroups of the limiting (stable) linear group GL() is given for an algebraically closed field of characteristic p. Every Sylow p-subgroup is characterized by a p-adic integer together with a finite or countable cardinal.     

表特殊线性群中元素为平延换位子之积

考虑元素了数大于3的域F上的特殊线性群SLnF.对GLnF中任一矩阵A,记resA为A－I的秩,称矩阵A为平延,如果resA=I并且 detA=1,对n≥2,本文证明SLnF中任一矩阵都可写成不超过[resA/2] 2个平延换位子之积。     

Linear Group over a Class of Ring R

Let R be a commutative ring^[1] with identical element 1 and maximal ideal M_i where i\in N and N is an ordered indieatrix set. Let the mapping $f:R\rightarrow \prod\limits_{i \in N} {R/{M_i}}$, be a ring homomorphism from R onto $[\prod\limits_{i \in N} {R/{M_i}} \]$, where $[\prod\limits_{i \in N} {R/{M_i}} \]$ is the direct product of residual fields B/M_i. In this paper, it is proved that if A \in GL_n(R), then A=BH_1……H_k-1, where res B=1 and H_1,\cdots, H_k-1 are the symmetries. Furthermore, the bound of the positive integer number K is investigated. In particular, the author gives the smallest number l(A) of symmetric factors in the products which expresses the elements of G_n= {A\in GLn(R)| det A=±l}. Consequently, the l(A) problems discussed in [2, 3, 4] are special cases of this paper.     

Linear Operators Preserving Symplectic Group over a Field Consisting of at Least Four Elements

Suppose F is a field consisting of at least four elements. Let Mn(F) and SP2n(F) be the linear space of all n×n matrices and the group of all 2n×2n symplectic matrices over F, respectively. A linear operator L:M2n(F)→M2n(F) is said to preserve the symplectic group if L(SP2n(F))=SP2n(F). It is shown that L is an invertible preserver of the symplectic group if and only if L takes the form (i) L(X)=QPXP-1 for any X∈M2n(F) or (ii) L(X)=QPXTP-1 for any X∈M2n(F), where Q∈SP2n(F) and P is a generalized symplectic matrix. This generalizes the result derived by Pierce in Canad J. Math., 3(1975), 715-724.     

Sets of Transvections Generating Subgroups Isomorphic to Special Linear Groups

ABSTRACT

The main result of this paper is a graph-theoretic necessary and sufficient condition, for a given set of transvections in SL(n, K) (n > 2 and K a finite field of characteristic not 2 or 3), to generate a group isomorphic to SL (m, L), for some m and some subfield L of K.     

单位上三角矩阵群的注记

记Tr_1(n,Z)是整数环Z上对角线元素全是1的全体上三角矩阵组成的群,k_(ij)(1≤i相似文献   

Multi-sequences with Almost Perfect Linear Complexity Profile and Function Fields over Finite Fields

Sequences with almost perfect linear complexity profile defined by Niederreiter (1997, Lecture Notes in Computer Science, Vol. 304, pp. 37–51, Springer-Verlag, Berlin/New York) are quite important for stream ciphers. In this paper, we investigate multi-sequences with almost perfect linear complexity profile and obtain a construction of such multi-sequences by using function fields over finite fields. Some interesting examples from this construction are presented to illustrate our construction.     

一类函数增量的局部渐近性质

文章研究了一类函数增量的局部渐近性质,发现这类函数增量的局部渐近性对于一元实函数,二元及多元实函数,向量值函数和复函数在一定条件下都会保持不变,进而提出了两个相关的猜想:此类函数增量的渐近性是关于函数变换的拓扑不变量。     

The Braid Group and Linear Rigidity

We introduce the BC-operation (short for braid-companion) on tuples of matrices. It corresponds to Katz's middle convolution operation on local systems, and generalizes it to fields K of arbitrary characteristic. It is based on the Burau–Gassner representation of the braid group. We expect many applications, in Galois theory (for finite K) as well as in Katz's original set-up of local systems and linear differential equations (where K = ).     

On Maximal Unipotent Subgroups of a Special Linear Group Over Commutative Ring

Ukrainian Mathematical Journal - It is proved that all maximal unipotent subgroups of a special linear group over commutative ring with identity (such that the factor ring of its modulo primitive...     

The mod 2 Homology of the General Linear Group of a 2-adic Local Field

Let F be a finite extension of the 2-adic rational numbers. We compute the mod 2 homology of the general linear group GL(F) as a Hopf algebra over the Steenrod algebra. The answer is formulated in terms of the well-known homology algebras of the infinite unitary group U, its classifying space BU, and the classifying space BO of the infinite orthogonal group.     

The Whitehead Group of the Novikov Ring

The Bass–Heller–Swan–Farrell–Hsiang–Siebenmann decomposition of the Whitehead group K ₁(A[z,z^-1]) of a twisted Laurent polynomial extension A[z,z^-1] of a ring A is generalized to a decomposition of the Whitehead group K ₁(A((z))) of a twisted Novikov ring of power series A((z))=A[[z]][z^-1]. The decomposition involves a summand W₁(A, ) which is an Abelian quotient of the multiplicative group W(A,) of Witt vectors 1+a₁z+a₂z²+ ··· A[[z]]. An example is constructed to show that in general the natural surjection W(A, )^ab W₁(A, ) is not an isomorphism.     

主理想整环上线性群中子群H_r的扩群

设R是一个主理想整环,GL(n,R)为R上n阶一般线性群,H_r为GL(n,R)的一个子群,在n≥3的情形下给出H_r在GL(n,R)中的所有扩群.     

The Euler Class Group of a Noetherian Ring

For a commutative Noetherian ring A of finite Krull dimension containing the field of rational numbers, an Abelian group called the Euler class group is defined. An element of this group is attached to a projective A-module of rank = dim A and it is shown that the vanishing of this element is necessary and sufficient for P to split off a free summand of rank 1. As one of the applications of this result, it is shown that for any n-dimensional real affine domain, a projective module of rank n (with trivial determinant), all of whose generic sections have n generated vanishing ideals, necessarily splits off a free direct summand of rank 1.     

On Non-Congruence Subgroups of the Analogue of the Modular Group in Characteristic p

Let k[t] be the polynomial ring over a finite field k. The group SL ₂(k[t]) is often referred to as the analogue, in characteristic p, of the classical modular group SL ₂( ), where is the ring of rational integers. It is well-known that the smallest index of a non-congruence subgroup of SL ₂( ) is 7. Here we compute this index for SL ₂(k[t]). (In all but 6 cases it turns out to be 1 + q, where q is the order of k.)