On the p-length of some finite p-soluble groups

The final publication is available at Springer via http://dx.doi.org/10.1007/s11856-014-1095-y 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 The research of the authors is supported by Proyecto MTM2010-19938-C03-01/03 of the Ministerio de Ciencia e Innovacion de Espana. The first author is also supported by Project of NSFC (11271085). Ballester-Bolinches, A.; Esteban Romero, R.; Ezquerro, LM. (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 A. Ballester-Bolinches, R. Esteban-Romero and M. Asaad, Products of Finite Groups, de Gruyter Expositions in Mathematics, Vol. 53, Walter de Gruyter, Berlin, 2010. A. Ballester-Bolinches, R. Esteban-Romero and L. M. Ezquerro, On a p-Schur-Frattini extension of a finite group, preprint. A. Ballester-Bolinches, L. M. Ezquerro and A. N. Skiba, On subgroups of hypercentral type of finite groups, Israel Journal of Mathematics 199 (2014), 259–265. A. Ballester-Bolinches and X. Guo, Some results on p-nilpotence and solubility of finite groups, Journal of Algebra 228 (2000), 491–496. K. Doerk and T. Hawkes, Finite Soluble Groups, de Gruyter Expositions in Mathematics, Vol. 4, Walter de Gruyter, Berlin, 1992. The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.5.7, 2012. J. González-Sánchez and T. S. Weigel, Finite p-central groups of height k, Israel Journal of Mathematics 181 (2011), 125–143. D. Gorenstein, Finite Groups, Harper & Row, New York, 1968. B. Huppert, Endliche Gruppen I, Grundlehren der Mathematischen Wissenschaften, Vol. 134, Springer-Verlag, Berlin-Heidelberg-New York, 1967. B. Huppert and N. Blackburn, Finite Groups II, Grundlehren der Mathematischen Wissenschaften, Vol. 242, Springer-Verlag, Berlin-Heidelberg-New York, 1982. B. Huppert and N. Blackburn, Finite Groups III, Grundlehren der Mathematischen Wissenschaften, Vol. 243, Springer-Verlag, Berlin-Heidelberg-New York, 1982. T. S. Weigel, Finite p-groups which determine p-nilpotency locally, Hokkaido Mathematical Journal 411 (2012), 11–29.