[EN] We give some sufficient conditions for a normal p-subgroup P of a finite group G to have every G-chief factor below it cyclic. The S-permutability of some p-subgroups of O^p(G)plays an important role. Some known results ...
[EN] The behaviour of totally permutable products of finite groups with respect to certain classes of groups is studied in the paper. The results are applied to obtain information about totally permutable products of T, ...
[EN] In the paper, a Frattini-like subgroup associated with a class X of simple groups is introduced and analysed. The corresponding X-saturated formations are exactly the X-local ones introduced by Förster. Our techniques ...
Esteban Romero, Ramón(Universitat de València - Servei de Publicacions, 1999)
In the first part, new bounds for the number of conjugacy classes of maximal length of a finite $p$-group $G$, $r(G)$, are obtained, and they are related with the length of these classes. If $r(G)=p^m-b-1$, there exists a ...
Ballester Bolinches, Adolfo; Beidleman, J. C.; Cossey, John; Esteban Romero, Ramón; Rangland, M. F.; Schmidt, Jack(Springer Verlag (Germany), 2009-06)
The aim of this paper is to prove certain characterization theorems
for groups in which permutability is a transitive relation, the so called
PT -groups. In particular, it is shown that the finite solvable PT -groups,
the ...
Ballester-Bolinches, A.; Beidleman, J.C.; Esteban Romero, Ramón(Cambridge University Press (CUP): STM Journals - No Cambridge Open, 2014-06)
All groups are finite. A subgroup H of a group G is called a primitive subgroup if it is a proper subgroup in the intersection of all subgroups of G containing H as its proper subgroup. He, Qiao and Wang [7] proved that ...
[EN] In this paper criteria for a product of formations to be X-local, X a class of simple groups, are obtained. Some classical results on products of saturated formations appear as particular cases.
Esteban Romero, Ramón; Vincenzi, Giovanni(University of Isfahan, 2018)
[EN] In this survey we highlight the relations between some subgroup embedding properties that characterise groups in which normality is a transitive relation in certain universes of groups with some finiteness properties.
[EN] This paper is devoted to the study of mutually permutable products of finite groups. A factorised group G=AB is said to be a mutually permutable product of its factors A and B when each factor permutes with every ...
Ballester-Bolinches, A.; Beidleman, J. C.; Esteban Romero, Ramón; Ragland, M. F.(Universitat Autonoma de Barcelona, 2016)
[EN] We call G a Hall_X -group if there exists a normal nilpotent subgroup N of G
for which G/N' is an X -group. We call G a T0 -group provided G/\Phi(G) is a T -group, that
is, one in which normality is a transitive ...
Ballester-Bolinches, A.; Beidleman, J. C.; Esteban Romero, Ramón; Ragland, M. F.(Elsevier, 2015-05)
[EN] In this survey paper several subgroup embedding properties related to some types of permutability
are introduced and studied.
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Liriano Castro, Orieta del Corazón de Jesús(Universitat Politècnica de València, 2016-01-07)
[EN] The scope of this thesis is the abstract finite group theory. All the groups we will consider will be finite. hence, the word "group" will be understood as a synonimous of "finite group". We say that a subgroup H of ...
[EN] An extension of the well-known Frobenius criterion of p-nilpotence in groups with modular Sylow p-subgroups is proved in the paper. This result is useful to get information about the classes of groups in which every ...
Ballester Bolinches, Adolfo; Esteban Romero, Ramón(Cambridge University Press, 2001-12)
[EN] In this paper a local version of Agrawal's theorem about the structure of finite groups in which Sylow permutability is transitive is given. The result is used to obtain new characterisations of this class of finite groups.
[EN] In this survey we present some significant bounds for the number of maximal subgroups of a given index of a finite group. As a consequence, new bounds for the number of random generators needed to generate a finite ...
Let Z be a complete set of Sylow subgroups of a finite group G, that is,
a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A
subgroup H of G is called Z-permutable if H permutes with all members ...