Main eigenvalues and automorphisms of a graph

We study some aspects of the relationship between algebras associated with graphs and automorphism groups. We study an algebra generated by the adjacent matrix of a graph and the all ones matrix, and derive a lower bound for the rank of the automorphism group of a graph. If a graph attains the equality in the above bound, it is calledextremal. We also describe some properties and examples of extremal graphs.     

Lie group structures on symmetry groups of principal bundles

In this paper we describe how one can obtain Lie group structures on the group of (vertical) bundle automorphisms for a locally convex principal bundle P over the compact manifold M. This is done by first considering Lie group structures on the group of vertical bundle automorphisms Gau(P). Then the full automorphism group Aut(P) is considered as an extension of the open subgroup DiffP(M) of diffeomorphisms of M preserving the equivalence class of P under pull-backs, by the gauge group Gau(P). We derive explicit conditions for the extensions of these Lie group structures, show the smoothness of some natural actions and relate our results to affine Kac-Moody algebras and groups.     

（广义）四元数群的自同构群及其全形

该文讨论了一类2^n阶非交换群——（广义）四元数群Q_{2^n}=〈a,b|a^{2^n-1}=1,b^2=a^{2^{n-2}},{b^{-1}ab=a^{-1}〉(n≥3)的自同构群A（Q_{2^n}）与全形H（Q_{2^n}））的置换表示，给出了A（Q_{2^n}））与H（Q_{2^n}））的构造.     

无限秩仿射李代数的cartan子代数的共轭性

本文给出了无限秩仿射李代数的某种类型的Cartan子代数的定义,并证明了这种Cartan子代数在无限秩仿射李代数的某种类型的自同构下的共轭性.     

自同构群阶为prq~2的有限群

本文给出满足|Aut(G)|=prq~2,q>2的有限群 G的完全分类。     

On perfect binary codes

Some results on perfect codes obtained during the last 6 years are discussed. The main methods to construct perfect codes such as the method of -components and the concatenation approach and their implementations to solve some important problems are analyzed. The solution of the ranks and kernels problem, the lower and upper bounds of the automorphism group order of a perfect code, spectral properties, diameter perfect codes, isometries of perfect codes and codes close to them by close-packed properties are considered.     

典型群PSU(3,q~2)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