Abstract
Let ℨ be a complete set of Sylow subgroups of a finite group G, that is, ℨ contains exactly one and only one Sylow p-subgroup of G for each prime p. A subgroup H of a finite group G is said to be ℨ-permutable if H permutes with every member of ℨ. The purpose of this article is to study the influence of ℨ-permutability of all maximal subgroups of the Sylow subgroups of the generalized Fitting subgroup of some normal subgroup of a finite group G on the structure of G. Our results improve and extend the main results of Asaad (
1998
), Asaad and Heliel (
2003
), Asaad et al. (
1991
), Li et al. (
2003
), Ramadan (
1992
), and Srinivasan (
1980
).