关键词: Sylow交, 块, 极大正规p-子群

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