Acta Scientiarum Naturalium Universitatis Pekinensis

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On Sylow Intersection Conjugacy Classes

WANG Baoshan   

  1. School of Science of Beihang University and Key Laboratory of Mathmatics, Informatics,
  • Received:2003-10-31 Online:2005-01-20 Published:2005-01-20

关于Sylow交的共轭类

王宝山   

  1. 北京航空航天大学理学院数学、信息与行为教育部重点实验室北京航空航天大学、北京大学,北京,100083,E-mail: bwang@buaa.edu.cn

Abstract: Suppose that G is a finite group and p is a prime such that p||G|. This paper studies the group invariant np(G), the number of G-orbits of Sylow intersections, which plays an important role in the research of block theory and indecomposable modules of finite groups. The paper shows some properties for finite groups with np(G)=2, in particular, it gives some necessary and sufficient conditions which show when a finite group G with np(G)=2 has the unique maximal normal p-subgroup as an intersection of two distinct Sylow p-subgroups.

Key words: sylow intersection, block, maximal normal p-subgroup

摘要: G为有限群,pG阶数的一个素因子,即p||G|。在有限群的研究中,Sylow p-子群无疑起到了非常重要的作用;同样,Sylow p-子群交在有限群不可分解模和块论研究当中的作用也是不容忽视的。文中研究了有限群G的 Sylow p-子群交的共轭类个数np(G)对于有限群结构的影响,并且着重讨论了np(G)=2的有限群的性质,特别地,给出了有限群G满足np(G)=2时2个不同Sylow p-子群的交与Op(G)相等的几个充分必要条件。

关键词: Sylow交, 块, 极大正规p-子群

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