Finite p-Groups All of Whose Minimal Nonnormal Subgroups Posses Large Normal Closures

We obtained some results about finite p-groups G with G/H^G being abelian for all nonnormal subgroups H, where H^G denotes the normal closure of H. Moreover, we give a classification of finite p-groups G with G/H^G being cyclic for all nonnormal subgroups H.     

Nearly s-Normality of Groups and Its Properties

We call a subgroup H of a group G nearly s-normal in G if there exists N ? G such that HN ? G and H ∩ N ≤ H _sG , where H _sG is the largest s-permutable subgroup of G contained in H. In this article, we obtain some results about the nearly s-normal subgroups and use them to characterize the structure of finite groups.     

Spreads, arcs, and multiple wavelength codes

We present several new families of multiple wavelength (2-dimensional) optical orthogonal codes (2D-OOCs) with ideal auto-correlation λ_a=0 (codes with at most one pulse per wavelength). We also provide a construction which yields multiple weight codes. All of our constructions produce codes that are either optimal with respect to the Johnson bound (J-optimal), or are asymptotically optimal and maximal. The constructions are based on certain pointsets in finite projective spaces of dimension k over GF(q) denoted PG(k,q).     

关于SQ-补子群

假定Fitting子群F(G)或广义Fitting子群F^*(G)的某些子群在G中SQ-补来研究包含超可解群的饱和群系s,这里G∈s.一些已知结果被推广.     

关于有限群的$CAP$-嵌入子群

A subgroup H of a finite group G is said to be CAP-embedded subgroup of G if, for each prime p dividing the order of H, there exists a CAP-subgroup K of G such that a Sylow p-subgroup of H is also a Sylow p-subgroup of K. In this paper some new results are obtained based on the assumption that some subgroups of prime power order have the CAP-embedded property in the group.     

非线性不可约特征标维数相等且为素数个的有限群

对于具有素数个非线性不可约特征标且它们的维数相等的有限群,我们给出一个分类.     

具有指数为2的循环子群的亚循环群

我们给出了具有指数为2的循环子群的亚循环群的同构分类.这个结果可应用于正则地图的研究中.     

The influence of X-semipermutability of subgroups on the structure of finite groups

Let A be a subgroup of a group G and X be a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we investigate further the influence of X-semipermutability of some subgroups on the structure of finite groups. Some new criteria for a group G to be supersoluble or p-nilpotent are obtained.     

The influence of <Emphasis Type="Italic">X</Emphasis>-semipermutability of subgroups on the structure of finite groups

Let A be a subgroup of a group G and X be a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we investigate further the influence of X-semipermutability of some subgroups on the structure of finite groups. Some new criteria for a group G to be supersoluble or p-nilpotent are obtained. This work was supported by National Natural Science Foundation of China (Grant Nos. 10771172, 10771180)