Abstract
Let 3 be a complete set of Sylow subgroups of a finite group G, that is, for each prime p dividing the order of G, 3 contains exactly one and only one Sylow p-subgroup of G. A subgroup H of a finite group G is said to be 3-permutable if 11 permutes with every member of 3. The purpose here is to study the influence of 3-permutability of some subgroups on the structure of finite groups. Some recent results are generalized.