<Emphasis Type="Italic">k</Emphasis>–Pyramidal One–Factorizations

We consider one–factorizations of complete graphs which possess an automorphism group fixing k ≥ 0 vertices and acting regularly (i.e., sharply transitively) on the others. Since the cases k = 0 and k = 1 are well known in literature, we study the case k≥ 2 in some detail. We prove that both k and the order of the group are even and the group necessarily contains k − 1 involutions. Constructions for some classes of groups are given. In particular we extend the result of [7]: let G be an abelian group of even order and with k − 1 involutions, a one–factorization of a complete graph admitting G as an automorphism group fixing k vertices and acting regularly on the others can be constructed.     

Cone-transitive matrix semigroups

Semigroups of matrices (over an ordered field) with non-negative entries are considered. A complete characterization is obtained for the semigroups which are minimal transitive on the positive (or non-negative) cone of the underlying vector space. Consequently, an explicit form for the semigroups sharply transitive on the cone is derived.     

Isometries of Quaternionic Lie Groups

We study connected Lie groups whose Lie algebra is obtained as the tensor product of a real associative algebra and the algebra of quaternions. It is proved that they carry a natural integrable -structure. We endow such quaternionic Lie groups with a left-invariant Hermitian metric and study the identity connected component of their isometry groups. The determination of such identity connected component is illustrated with a family of examples.     

Endomorphisms of superelliptic jacobians

Let K be a field of characteristic zero, n ≥ 5 an integer, f(x) an irreducible polynomial over K of degree n, whose Galois group contains a doubly transitive simple non-abelian group. Let p be an odd prime, the ring of integers in the pth cyclotomic field, C _{f, p} : y ^p  =  f(x) the corresponding superelliptic curve and J(C _{f, p} ) its jacobian. Assuming that either n  =  p + 1 or p does not divide n(n  −  1), we prove that the ring of all endomorphisms of J(C _{f, p} ) coincides with . The same is true if n  =  4, the Galois group of f(x) is the full symmetric group S ₄ and K contains a primitive pth root of unity. An erratum to this article can be found at     

Discreteness Criterions of Isometric Subgroups for Quaternionic Hyperbolic Space

In this paper, we give analogue of Jörgensen's inequality for nonelementary groups of isometries of complex hyperbolic 2-space generated by two elements, one of which is either loxodromic or boundary elliptic for the same group of isometries of quaternionic hyperbolic 2-space. And we give a sufficient condition for a nonelementary subgroup of isometries of quaternionic hyperbolic 2-space generated by two elements one of which is parabolic not to be discrete.     

每个子群都c-正规的有限群

在本文中我们研究有限CN-群, 即每个子群都c-正规的有限群. 我们得到以下结果:群G是CN-群当且仅当G^∈的每个子群都在G中正规.群G是CN-群当且仅当G可解且c-正规性是传递的.设p是一个奇素数, P是一个p-群, 则P是一个CN-群当且仅当Φ(P)≤Z(P).我们也得到了一些CN-群的直积为CN-群的判别条件.     

Finite groups with transitive semipermutability

A group G is said to be a T-group (resp. PT-group, PST-group), if normality (resp. permutability, S-permutability) is a transitive relation. In this paper, we get the characterization of finite solvable PST-groups. We also give a new characterization of finite solvable PT-groups.      

The L-sharp permutation groups

An answer is given to a problem proposed by Bannai and Ito for {l,l+s,l+s+t}-sharp permutation group, and the result is used to determine L-sharp groups for L={l,l+1,l+3}and{l,l+2,l+3}.     

TheL-sharp permutation groups

An answer is given to a problem proposed by Bannai and Ito for {I, I + s, I + s + t}-sharp permutation group, and the result is used to determineL-sharp groups for L={I, I + 1, I + 3} and {I, I + 2, I + 3}.     

计算机代数用于有限群的计算

本用Mathematica语言研究置换群运算的计算机实现．并进而实现对于给定的n，设计判断交代群An是否为单群的程序．