【摘要】 设G为有限群 ,p是G阶数的一个素因子 ,即p| |G|。在有限群的研究中 ,Sylowp 子群无疑起到了非常重要的作用 ;同样 ,Sylowp 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Sylowp 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Sylowp 子群的交与Op(G)相等的几个充分必要条件。更多还原

【Abstract】 Suppose that G is a finite group and p is a prime such that p||G|.This paper studies the group invariant n p(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 n p(G)=2, in particular, it gives some necessary and sufficient conditions which show when a finite group G with n p(G)=2 has the unique maximal normal p-subgroup as an intersection of two distinct Sylow p-subgroups.更多还原