Abstract
Let 3 be a complete set of Sylow subgroups of a finite group G, that is, a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A subgroup H of G is called 3-S-semipermutable if H permutes with every Sylow p-subgroup of G in 3 for all p is not an element of pi(H); H is said to be 3-S-seminormal if it is normalized by every Sylow p-subgroup of G in 3 for all p is not an element of pi(H). The main aim of this paper is to characterize the 3-MS-groups, or groups G in which the maximal subgroups of every Sylow subgroup in 3 are 3-S-semipermutable in G and the 3-MSN-groups, or groups in which the maximal subgroups of every Sylow subgroup in 3 are 3-S-seminormal in G.