A note on the solvability of groups

AbstractLet M be a maximal subgroup of a finite group G and K/L be a chief factor such that L⩽M while K⊈M. We call the group M∩K/L a c-section of M. And we define Sec(M) to be the abstract group that is isomorphic to a c-section of M. For every maximal subgroup M of G, assume that Sec(M) is supersolvable. Then any composition factor of G is isomorphic to L2(p) or Zq, where p and q are primes, and p≡±1(mod 8). This result answer a question posed by [Y. Wang, S. Li, c-Sections of maximal subgroups of finite groups, J. Algebra 229 (2000) 86–94]