ABSTRACT
Let G be a finite group and n be a positive integer. An n-minimal subgroup H of G is called to be exactly n-minimal if no proper subgroup of H is n-minimal. In this paper, we study the solvability of G under the assumption that all exactly n-minimal subgroups of G are S-permutable.
Acknowledgments
The author thanks Professor Xianhua Li and Professor Guohua Qian for their encouragements and also thanks Dr. Tianze Li for his helpful discussions.