Ballester Bolinches, Adolfo; Beidleman, James C.; Esteban Romero, Ramón(Elsevier, 2007-06-01)
[EN] Finite groups G for which for every subgroup H and for all primes q dividing the index |G:H| there exists a subgroup K of G such that H is contained in K and |K:H|=q are called Y-groups. Groups in which subnormal ...
We study finite groups in which every maximal subgroup is
supersoluble or normal. Our results answer some questions arising from
papers of Asaad and Rose.
Ballester Bolinches, Adolfo; Cossey, John; Pedraza Aguilera, María Carmen(Elsevier, 2016-11-16)
In this paper we obtain some bounds for the exponent of a finite group, and its derived subgroup, which is a mutually permutable product of two abelian subgroups. They improve the ones known for products of finite abelian ...
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 ...
[EN] A group G has finite (or Prufer or special) rank if every finitely generated subgroup of G can be generated by r elements and r is the least integer with this property. The aim of this paper is to prove the following ...
[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, ...
Ballester-Bolinches, A.; Cossey, J.; Madanha, S. Y.; Pedraza Aguilera, María Carmen(Springer-Verlag, 2024-02)
[EN] We say a group G = AB is the totally semipermutable product of subgroups A and B if every Sylow subgroup P of A is totally permutable with every Sylow subgroup Q of B whenever gcd(|P|,|Q|)=1\documentclass[12pt]{minimal} ...
[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 ...
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 ...
We continue here our study of pairwise mutually and pairwise totally permutable
products. We are looking for subgroups of the product in which the given factorization
induces a factorization of the subgroup. In the case ...
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.
[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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[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.
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 ...