A class of generalized supersoluble groups

This paper is devoted to the study of groups G in the universe cL of all radical locally finite groups with min-p for all primes p such that every [delta]-chief factor of G is either a cyclic group of prime order or a quasicyclic group. We show that within the universe cL this class of groups behaves very much as the class of finite supersoluble groups

On metacyclic subgroups of finite groups

‎The aim of this survey article is to present some structural results about of groups whose Sylow p-subgroups are metacylic (p a prime)‎. ‎A complete characterisation of non-nilpotent groups whose 2-generator subgroups are metacyclic is also presented‎

On minimal non-supersoluble groups

This paper has been published in Revista Matemática Iberoamericana, 23(1):127-142 (2007). Copyright 2007 by Real Sociedad Matemática Española and European Mathematical Society Publishing House. The final publication is available at http://rmi.rsme.es http://www.ems-ph.org/journals/journal.php?jrn=rmi http://projecteuclid.org/euclid.rmi/1180728887[EN] The aim of this paper is to classify the finite minimal non-p-supersoluble groups, p a prime number, in the p-soluble universe.Supported by Proyecto BFM2001-1667-C03-03 (MCyT) and FEDER (European Union)Ballester Bolinches, A.; Esteban Romero, R. (2007). On minimal non-supersoluble groups. Revista Matemática Iberoamericana. 1(23). http://hdl.handle.net/10251/1847712

On finite soluble groups in which Sylow permutability is a transitive relation

This paper has been published by Springer-Verlag and Akadémiai Kiadó in Acta Mathematica Hungarica, 101(3):193-202 (2003). The final publication is available at http://www.springerlink.com http://dx.doi.org/10.1023/B:AMHU.0000003903.71033.fcA characterisation of finite soluble groups in which Sylow permutability is a transitive relation by means of subgroup embedding properties enjoyed by all the subgroups is proved in the paper. The key point is an extension of a subnormality criterion due to Wielandt.http://dx.doi.org/10.1023/B:AMHU.0000003903.71033.fcBallester Bolinches, A.; Esteban Romero, R. (2003). On finite soluble groups in which Sylow permutability is a transitive relation. 3(101). doi:10.1023/B:AMHU.0000003903.71033.fc310

On finite groups generated by strongly cosubnormal subgroups

This paper has been published in Journal of Algebra, 259(1):226-234 (2003). Copyright 2003 by Elsevier. http://dx.doi.org/10.1016/S0021-8693(02)00535-5[EN] Two subgroups A and B of a group G are cosubnormal if A and B are subnormal in their join and are strongly cosubnormal if every subgroup of A is cosubnormal with every subgroup of B. We find necessary and sufficient conditions for A and B to be strongly cosubnormal in and, if Z is the hypercentre of G=, we show that A and B are strongly cosubnormal if and only if G/Z is the direct product of AZ/Z and BZ/Z. We also show that projectors and residuals for certain formations can easily be constructed in such a group. Two subgroups A and B of a group G are N-connected if every cyclic subgroup of A is cosubnormal with every cyclic subgroup of B (N denotes the class of nilpotent groups). Though the concepts of strong cosubnormality and N-connectedness are clearly closely related, we give an example to show that they are not equivalent. We note, however, that if G is the product of the N-connected subgroups A and B, then A and B are strongly cosubnormal.The first and the third authors have been supported by Proyecto BFM2001-1667-C03-03 from Ministerio de Ciencia y Tecnolog´ıa, Spain. The third author has been supported by a grant from the Program of Support of Research (Stays of Researchers in other academic institutions) of the Universitat Polit`ecnica de Val`encia. Part of this research has been carried out during a visit of the third author to the School of Mathematical Sciences of the Australian National University in Canberra (Australia), to whom he wants to express his gratitude for their kindness and financial support.Ballester Bolinches, A.; Cossey, J.; Esteban Romero, R. (2003). On finite groups generated by strongly cosubnormal subgroups. Journal of Algebra. 1(259):226-234. doi:10.1016/S0021-8693(02)00535-5226234125

Graphs and classes of finite groups

There are different ways to associate to a finite group a certain graph. An interesting question is to analyse the relations between the structure of the group, given in group-theoretical terms, and the structure of the graph, given in the language of graph theory. This survey paper presents some contributions to this research line

Formations of finite monoids and formal languages: Eilenberg's variety theorem revisited

We present an extension of Eilenberg's variety theorem, a well-known result connecting algebra to formal languages. We prove that there is a bijective correspondence between formations of finite monoids and certain classes of languages, the formations of languages. Our result permits to treat classes of finite monoids which are not necessarily closed under taking submonoids, contrary to the original theory. We also prove a similar result for ordered monoids.The authors are supported by Proyecto MTM2010-19938-C03-01 from MICINN (Spain). The second author is supported by the project ANR 2010 BLAN 0202 02 FREC. The third author was supported by the Grant PAID-02-09 from Universitat Politècnica de València

On large orbits of subgroups of linear groups

The main aim of this paper is to prove an orbit theorem and to apply it to obtain a result that can be regarded as a significant step towards the solution of Gluck's conjecture on large character degrees of finite solvable groups