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.

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

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，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n_p(G)对于有限群结构的影响，并且着重讨论了n_p(G)=2的有限群的性质，特别地，给出了有限群G满足n_p(G)=2时2个不同Sylow p-子群的交与O_p(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