交换自同构群的若干结果

借助于环论的方法研究了具有交换自同构群的有限群,提出了一种新的自同构构作技术,并用之证明了这样的非交换有限群具有非循环的中心子群,以及其每个极大子群的中心子群也都非循环.     

Curran猜想的解答

本文确定了能作为有限群自同构群的Ｐ－群的最佳下最，彻底解决了Ｃｕｒｒａｎ在１９８９年提出的关于此最佳下界的三个猜想。     

Phase-fixed double-group 3-Γ symbols. IV. Real 3-Γ symbols and coupling coefficients for the group hierarchies T* ⊃ C 3 * and T* ⊃ C 2 *

We present sets of real 3- symbols which correspond to explicitly given irreducible matrix representations for the two double group hierarchies T* C ₃ ^* and T* C ₂ ^* . They fit into the formalism exposed in a previous paper [1] on the general theory of 3- symbols and coupling coefficients and illustrate much of the discussion in a subsequent one [2] treating the particular properties of the double groups.     

有限CN-p-群

每个子群都C-正规的有限群称为CN-群.本文首先给出二元生成的CN-p-群的完全分类.在此基础上得到CN-p-群的结构:当p为奇素数时,有限群G为CNp-群当且仅当G的每个元都平凡地作用在Φ(G)上;有限群G为CN-2-群当且仅当对任意给定的a∈G,都有对任意g∈Φ(G),g~a=g或者对任意g∈Φ(G),g~a=g~(-1).最后给出两个CN-p-群的直积是CN-p-群的判定条件.     

Invertible Linear Maps on the General Linear Lie Algebras Preserving Solvability

Let Mn be the algebra of all n × n complex matrices and gl(n,C) be the general linear Lie algebra,where n ≥ 2.An invertible linear map ?:gl(n,C) →gl(n,C) preserves solvability in both directions if bot...     

Notes on Automorphisms of Prime Rings

Let R be a prime ring, L a noncentral Lie ideal and σ a nontrivial automorphism of R such that usσ(u)ut= 0 for all u ∈ L, where s, t are fixed non-negative integers. If either char R s + t or char R = 0, then R satisfies s4, the standard identity in four variables. We also examine the identity(σ([x, y])-[x, y])n=0 for all x, y ∈ I, where I is a nonzero ideal of R and n is a fixed positive integer. If either char R n or char R = 0, then R is commutative.     

The Order of Automorphisms of Quasigroups

We prove quadratic upper bounds on the order of any autotopism of a quasigroup or Latin square, and hence also on the order of any automorphism of a Steiner triple system or 1‐factorization of a complete graph. A corollary is that a permutation σ chosen uniformly at random from the symmetric group will almost surely not be an automorphism of a Steiner triple system of order n, a quasigroup of order n or a 1‐factorization of the complete graph . Nor will σ be one component of an autotopism for any Latin square of order n. For groups of order n it is known that automorphisms must have order less than n, but we show that quasigroups of order n can have automorphisms of order greater than n. The smallest such quasigroup has order 7034. We also show that quasigroups of prime order can possess autotopisms that consist of three permutations with different cycle structures. Our results answer three questions originally posed by D.  Stones.     

开关图的几个代数性质

首先对开关图的自同构群进行了研究,随即讨论了它的点传递性,并得到Calyley图的开关图依然是Cayley图.