某些MI群

主要分类了亚循环的MI群及MA群,超特殊的MI群及MA群,并给出了一些一般的MI群和MA群的例子．     

Finite p-Groups All of Whose Proper Quotient Groups are Abelian or Inner-Abelian

In this article, finite p-groups all of whose proper quotient groups are abelian or inner-abelian are classified. As a corollary, finite p-group all of whose proper quotient groups are abelian, and finite p-groups all of whose proper sections are abelian or inner-abelian are also classified.     

On maximal abelian subgroups in finite 2-groups

We determine here up to isomorphism the structure of any finite nonabelian 2-group G in which every two distinct maximal abelian subgroups have cyclic intersection. We obtain five infinite classes of such 2-groups (Theorem 1.1). This solves for p = 2 the problem Nr. 521 stated by Berkovich (in preparation). The more general problem Nr. 258 stated by Berkovich (in preparation) about the structure of finite nonabelian p-groups G such that A ∩ B = Z(G) for every two distinct maximal abelian subgroups A and B is treated in Theorems 3.1 and 3.2. In Corollary 3.3 we get a new result for an arbitrary finite 2-group. As an application of Theorems 3.1 and 3.2, we solve for p = 2 a problem of Heineken-Mann (Problem Nr. 169 stated in Berkovich, in preparation), classifying finite 2-groups G such that A/Z(G) is cyclic for each maximal abelian subgroup A (Theorem 4.1).      

Harborth constants for certain classes of metacyclic groups

The Harborth constant of a finite group $G$ is the smallest integer $k\ge exp\left(G\right)$ such that any subset of $G$ of size $k$ contains $exp\left(G\right)$ distinct elements whose product is 1. Generalizing previous work on the Harborth constants of dihedral groups, we compute the Harborth constants for the metacyclic groups of the form $H_{n,m}=〈x,y\mid x^n=1,y^2=x^m,yx=x^{?1}y〉$. We also solve the “inverse” problem of characterizing all smaller subsets that do not contain $exp\left(H_{n,m}\right)$ distinct elements whose product is 1.     

3p阶亚循环群的连通4度Cayley图

研究3p阶(p是大于3的素数)亚循环群的连通4度Cayley图.主要决定了其全自同构群的结构,并由此得到这类图的CI性、正规性和弧传递性.用到单群分类定理.     

21阶亚循环群的弱3-DCI性

本文证明21阶亚循环群G不是弱3-DCI群,否定了Babai和Frankl的一个猜测.此外还决定了群G的所有3元生成子集的CI-性.     

六阶图G与Sn的积图的交叉数

确定图的交叉数是NP．完全问题．目前已确定交叉数的六阶图与星图的笛卡尔积图极少。本文确定了—个六阶图G与星图5k积图的交叉数为Z（6,n）＋2n＋[n/2].     

群的融合自由积的πn-Frattini子群和πc-Frattini子群

Azarian M K将Tang C Y得到的关于两个群的带循环融合自由积的Frattini子群的一个定理推广到任意多个子群的带循环融合自由积的情况.通过考虑任意多个子群的带循环融合自由积的πnFrattini子群和πcFrattini子群,得到了类似的结果.     

特殊奇Hamiltonian模李超代数偶部的低维上同调群

利用了一个适当环面的权空间分解完全确定了从有限维特殊奇Hamiltonian模李超代数偶部到广义Witt超代数偶部的导子空间,进而给出了相应的低维上同调空间的维数公式.     

The Subgroup Normalizer Problem for Integral Group Rings of Some Nilpotent and Metacyclic Groups

For a group G and a subgroup H of G, this article discusses the normalizer of H in the units of a group ring RG. We prove that H is only normalized by the “obvious” units, namely products of elements of G normalizing H and units of RG centralizing H, provided H is cyclic. Moreover, we show that the normalizers of all subgroups of certain nilpotent and metacyclic groups in the corresponding group rings are as small as possible. These classes contain all dihedral groups, all finite nilpotent groups, and all finite groups with all Sylow subgroups being cyclic.