Open Access
On the p-length of some finite p-soluble groups
(Springer, 2014) Ballester Bolinches, Adolfo; Esteban Romero, Ramón; Ezquerro Marín, Luis Miguel; Matemáticas; Matematika
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.
Open Access
Real elements and p-nilpotence of finite groups
(Aracne, 2016) Ballester Bolinches, Adolfo; Esteban Romero, Ramón; Ezquerro Marín, Luis Miguel; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
Our first main result proves that every element of order 4 of a Sylow 2-subgroup S of a minimal non-2-nilpotent group G, is a real element of S. This allows to give a character-free proof of a theorem due to Isaacs and Navarro (see [9, Theorem B]). As an application, the authors show a common extension of the p-nilpotence criteria proved in [3] and [9].

Ezquerro Marín, Luis Miguel

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