关于A_(n-1)型CHEVALLEY扩群■的唯一性

本文讨论[1]中留下的A_(n-1)型Chevalley群G≌SL_n(K)的扩群G的唯一性问题,得到群G在同构意义下至多有1/2φ(n)个。     

Chevalley群中Levi子群在抛物子群中的扩群

本文以根系及Ｗｅｙｌ群为基础,以换位子公式为工具,对任意域上任意类型Ｃｈｅｖａｌｌｅｙ群,针对极大抛物子群情形,确定了Ｌｅｖｉ子群在抛物子群中的所有扩群．     

Levi子群L_α(n(α)=1)在Chevalley群G(Φ,F)中的扩群

设 Ｌ是复数域上单李代数，具有不可约根系 φ，固定基Ⅱ．设 Ｆ是一个特征不为２的域，且不是三元域，Ｇ（φ，Ｆ）是 Ｆ上φ型的 Ｃｈｅｖａｌｌｅｙ群．设 α∈Ⅱ，φα表示φ的一种类型子根系．当ｎ（α）＝１；且φ是Ｂｌ（ｌ ３），Ｄｌ（ｌ ４），Ｅ６，Ｅ７，或 Ｅ８之一时，本文决定了 Ｌｅｖｉ子群 Ｌα在 Ｇ（φ，Ｆ）中的所有扩群．     

Levi子群Lα(n(α)=1)在Chevalley群G(Ф,F)中的扩群

设L是复数域上单李代数,具有不可约根系Ф,固定基П.设F是一个特征不为2的域,且不是三元域,G(Ф,F)是F上Ф型的Chevalley群.设α∈П,Фα表示Ф的一种类型子根系.当n(α)=1,且Ф是Bl(l≥3),Dl(l ≥ 4),E6,E7,或E8之一时,本文决定了Levi子群Lα在G(Ф,F)中的所有扩群.     

有限域上Bl型Chevalley群的二元生成

证明了有限域上Bl型Chevalley群可由两个元素生成     

Chevalley群的一类子群的研究

设G＝L（F）是特征不为2的域F上Chevalley群,型为B1（l≥4）,Cl（l≥3）,Dl（l≥5）,E6,E7,E8或F4之一．当L（F）型为B4或F4时还假设F=F2设Lα1是L（F）的一类Levy子群．本文决定Lα1的正规化子在L（F）中的极大性．     

D1和E6型Weyl群的扭子群的扩群

本决定了D1和E6型Weyl群扭子群的所有扩群，这为确定相应Chevalley群扭子群的所有扩群奠定了基础。     

有限域上F4和G2型Chevalley群的二元生成

本文证明了有限域上F4和G2型Chevalley群均可由两个元素生成.     

有限Chevalley群作用下的子代数轨道生成的格

讨论了一般情形Chevalley群作用下的子代数轨道生成的格.在同类型格中,研究了不同格之间的包含关系,并对格中子代数的特性及格的几何性进行了刻画.     

有限域上型$B_n$的Chevalley群之间的同态

研究了特征为$p$的有限域上型$B_{n}$的Chevalley群的结构,并确定了特征为$p \ (p\neq 2)$的有限域上型$B_{n}$的Chevalley群 之间的非平凡同态.     

Homomorphisms between the chevalley groups over any fields of characteristic zero

Given an irreducible root system ∑, let G(F,L) denote the Cheval- ley group over a field F corresponding to a lattice L between the root lattice and the weight lattice of ∑,. We will determine all nontnvial homomorphisms from G(k,L ₁) to G(K,L ₂when k and K are any fields of characteristic zero, and we will verify that any nontrivial homomorphism from G(k,L ₁) to G(K,L ₂are induced by a field homomorphism from k to K by multiplying an automorphism of G(K,L ₂.     

Isomorphisms of adjoint Chevalley groups over integral domains

It is shown that every automorphism of an adjoint Chevalley group over an integral domain containing the rational number field is uniquely expressible as the product of a ring automorphism, a graph automorphism and an inner automorphism while every isomorphism between simple adjoint Chevalley groups can be expressed uniquely as the product of a ring isomorphism, a graph isomorphism and an inner automorphism. The isomorphisms between the elementary subgroups are also found having analogous expressions.

     

Unitary groups and ramified extensions

We classify all non-degenerate skew-hermitian forms defined over certain local rings, not necessarily commutative, and study some of the fundamental properties of the associated unitary groups, including their orders when the ring in question is finite.     

拟L商群的同态与同构

HX群是由一个群向其幂集上提升的群结构．文[1]将HX群推广到一类特殊的格-原子格L上,称之为AHX群．本文研究了一类特殊的AHX群-拟L商群的同态与同构,获得与拟商群相类似的结果．     

Dihedral side extensions and class groups

We present a non-abelian mirror-type principle relating the p-ranks of class groups of subfields of a dihedral field of degree 2p for an odd prime p with a limited ramification condition.     

On automorphism groups of some finite groups

We show that if n > 1 is odd and has no divisor p4 for any prime p, then there is no finite group G such that│Aut(G)│ = n.     

Turing degrees of nonabelian groups

For a countable structure , the (Turing) degree spectrum of is the set of all Turing degrees of its isomorphic copies. If the degree spectrum of has the least degree , then we say that is the (Turing) degree of the isomorphism type of . So far, degrees of the isomorphism types have been studied for abelian and metabelian groups. Here, we focus on highly nonabelian groups. We show that there are various centerless groups whose isomorphism types have arbitrary Turing degrees. We also show that there are various centerless groups whose isomorphism types do not have Turing degrees.