基于吴方法判断代数集上多项式自同态是否为同构

给出仿射代数集上多项式自同态为同构的Ｇｒｏｂｎｅｒ基准则,井利用Ｗｕ－Ｒｉｔｔ算法进行了计算,同时给出一些具体例子．     

O-2-transitive automorphism groups with abelian stabilizer of a point

It is proved that an o-2-transitive group of order automorphisms of a totally ordered set with Abelian stabilizer of a point is the permutation groupF={φ(a, b)‖a, bεP, a>0, (x)φ(a, b)=xa+b forxεP} of a totally ordered fieldP. Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 289–293, February, 1999.     

The conjugacy problem for Dehn twist automorphisms of free groups

A Dehn twist automorphism of a group G is an automorphism which can be given (as specified below) in terms of a graph-of-groups decomposition of G with infinite cyclic edge groups. The classic example is that of an automorphism of the fundamental group of a surface which is induced by a Dehn twist homeomorphism of the surface. For , a non-abelian free group of finite rank n, a normal form for Dehn twist is developed, and it is shown that this can be used to solve the conjugacy problem for Dehn twist automorphisms of . Received: February 12, 1996.     

A new symmetric design with parameters (176, 50, 14)

A new symmetric non‐self‐dual design with parameters (176, 50, 14) is constructed, where its full automorphism group of order 1000 is a faithful extension of the non‐abelian group of order 125 and exponent 5 by the cyclic group of order 8. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 387–390, 2000     

New coverings of t-sets with (t + 1)-sets

The minimum number of k-subsets out of a v-set such that each t-set is contained in at least one k-set is denoted by C(v, k, t). In this article, a computer search for finding good such covering designs, leading to new upper bounds on C(v, k, t), is considered. The search is facilitated by predetermining automorphisms of desired covering designs. A stochastic heuristic search (embedded in the general framework of tabu search) is then used to find appropriate sets of orbits. A table of upper bounds on C(v, t + 1, t) for v 28 and t 8 is given, and the new covering designs are listed. © 1999 John Wiley & Sons, Inc. J. Combin Designs 7: 217–226, 1999     

Flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1 and alternating socle

Consider the flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1. We prove that if {D} is a nontrivial 2-(v, k, λ) symmetric design with (k, λ) = 1 and G≤Aut({D}) is flag-transitive with Soc(G) = A_n for n≥5, then {D} is the projective space PG₂(3,2) and G = A₇.     

Strictly nontame primitive elements of the free metabelian Lie algebra of rank 3

We prove that the free metabelian Lie algebra M ₃ of rank 3 over an arbitrary field K admits strictly nontame primitive elements.     

C~3中一类拟凸超曲面的局部全纯自同构

给出了C~3中一类拟凸超曲面定义在原点邻域内的实解析无穷小CR自同构,并得到了这类超曲面在原点处稳定群的单位连通分支.     

1-quasiconformal mappings on a （2,2）-type quadric

This paper gets the Beltrami equations satisfied by a 1-quasiconformal mapping, which are exactly CR or anti-CR equations on （2,2）-type quadric Q0. This means a 1-quasiconformal mapping on Q0 is CR or anti-CR. This reduces the determination of 1- quasiconformal mappings to a problem on the theory of several complex analysis. The result about the group of CR automorphisms is used to determine the unit component of group of 1-quasiconformal mappings.     

Finite groups with its power automorphism groups having small indices

In this paper, a finite group G with IAut（G） ： P（G）I ~- p or pq is determined, where P（G） is the power automorphism group of G, and p, q are distinct primes. Especially, we prove that a finite group G satisfies ｜Aut（G） ： P（G）｜= pq if and only if Aut（G）/P（G） ≌S3. Also, some other classes of finite groups are investigated and classified, which are necessary for the proof of our main results.