外文翻译-有限幂零群的一个特征条件.docVIP

本科毕业设计 外文文献及译文 文献、资料题目：A characteristic condition of finite nilpotent group 文献、资料来源：LI Yang-ming / Li / J Zhejiang Univ SCI 2004 5(7):749-753 文献、资料发表（出版）日期： 院 （部）： 理学院 专 业： 信息与计算科学 班 级： 姓 名： 学 号： 指导教师： 翻译日期： 外文文献： A characteristic condition of finite nilpotent group LI Yang-ming (李样明) (Department of Mathematics, Zhejiang University, Hangzhou 310016, China) (Department of Mathematics, Guangdong College of Education, Guangzhou 510310, China) E-mail: liyangming@ Received Nov. 4, 2003; revision accepted Feb. 9, 2004 Abstract: This paper gives a characteristic condition of finite nilpotent group under the assumption that all minimal subgroups of G are well-suited in G. Key words: Z-permutable subgroup, Nilpotent group, The generalized Fitting subgroup, Hypercenter subgroup Document code: A CLC number: O152 INTRODUCTION In this paper, all groups considered are finite;G means a finite group. We use conventional notions and notations,as in Huppert(1968).Recall that a minimal subgroup of a finite group is a subgroup of prime order. For the group of even order, it is helpful to also consider the cyclic subgroup of order 4. Two subgroups H and K of a group G are said to permute if HK=KH.It is easily seen that H and K permute if and only if the set of HK is a subgroup of G. We know that a normal subgroup of G permutes with every subgroup of G. So Ore(1937) extended normal subgroup to quasinormal subgroup, a subgroup of G is called quasinormal subgroup of G if it permutes with every subgroup of G. Kegel (1962) went further to define Л-quasinormal subgroup, a subgroup of G is Л-quasinormal in G if it permutes with every Sylow subgroup of G. Recently, Asaad and Heliel(2003) extended Л-quasinormality to a new embedding property, namely the Z-permutability.Z is called a complete set of Sylow subgroups of G if for each prime p∈Л(G)(the set of distinct primes dividing |G|),Z contains exactly one Sylow p-subgroup of G,Gp say.A subgrou