Some sufficient conditions on the number of non-Abelian subgroups of a finite group to be solvable. (Q546334)

One of Thompson's theorems indicates that a finite group with a nilpotent maximal subgroup of odd order is solvable [see \textit{J. G. Thompson}, Math. Z. 72, 332-354 (1960; Zbl 0098.02003)]. As an important application of Thompson's above theorem, a finite group is solvable if it has an Abelian maximal subgroup. In this paper, the authors give some sufficient conditions on the number of non-Abelian subgroups of a finite group to be solvable.