The main aim of this paper is to give structural information of a finite group of minimal order belonging to a subgroup-closed class of finite groups and whose p-length is greater than 1, p a prime number. Alternative proofs and improvements of recent results about the influence of minimal p-subgroups on the p-nilpotence and p-length of a finite group arise as consequences of our study.
Ballester-Bolinches, A., Esteban-Romero, R., & Ezquerro, L. M. (2014). On the p-length of some finite p-soluble groups. Israel Journal of Mathematics, 204(1), 359–371. https://doi.org/10.1007/s11856-014-1095-y