Ballester Bolinches, Adolfo; Cossey, John; Esteban Romero, Ramón(Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, 2009)
[EN] There are different ways to associate to a group a
certain graph. In this context, it is interesting to ask for the relations
between the structure of the group, given in group-theoretical
terms, and the structure ...
Ballester Bolinches, Adolfo; Esteban Romero, Ramón; Ragland, Matthew F.(Walter de Gruyter, 2007-03)
[EN] A finite group G is said to be a PST-group if, for subgroups H and K of G with H Sylow-permutable in K and K Sylow-permutable in G, it is always the case that H is Sylow-permutable in G. A group G is a T*-group if, ...
[EN] It is shown in this paper that if X is a class of simple groups such that pi(X) = char X, the X-saturated formation H generated by a finite group cannot be expressed as the Gaschütz product F o G of two non-X-saturated ...
Ballester Bolinches, Adolfo; Esteban Romero, Ramón; Li, Yangming(Springer and Science China Press, 2012-05)
A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids every chief factor of the series. The structural impact of the partial cover and avoidance ...
Ballester Bolinches, Adolfo; Cosme-Llópez, E.; Esteban Romero, Ramón; Rutten, J.J.M.M.(Alexandru Ioan Cuza University of Iasi, 2015)
The main goal in this paper is to use a dual equivalence in automata theory started in [25] and developed in [3] to prove a general version of the Eilenberg-type theorem presented in [4]. Our principal results confirm the ...
A classical result of Gaschütz affirms that given a finite A-generated group G and a prime p, there exists a group G# and an epimorphism phi: G# ---> G whose kernel is an elementary abelian p-group which is universal among ...
Ballester Bolinches, Adolfo; Esteban Romero, Ramón; Jiang, Qinhui; Li, Xianhua(SpringerFondazione Annali di Matematica Pura ed Applicata, 2015-02)
In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An A 5 -free group possessing one of these families is soluble, and soluble groups with this property have ...
[EN] Let p be a prime. The class of all p-soluble groups G such that every p-chief factor of G is cyclic and all p-chief factors of G are G-isomorphic is studied in this paper. Some results on T-, PT-, and
PST -groups are ...
For a finite group G we define the graph $\Gamma(G)$ to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes $\{\mathcal {A}, \mathcal {B}\}$ are joined by an edge if for ...
[EN] In [J. C. Beidleman, D. J. S. Robinson, J. Algebra 1997, 191, 686--703, Theorem A], Beidleman and Robinson proved that if a group satisfies the permutizer condition, it is soluble, its chief factors have order a prime ...
[EN] Two subgroups A and B of a group G are cosubnormal if A and B are subnormal in their join <A,B> and are strongly cosubnormal if every subgroup of A is cosubnormal with every subgroup of B. We find necessary and ...
[EN] A critical group for a class of groups X is a minimal non-X-group. The critical groups are determined for various classes of finite groups. As a consequence, a classification of the minimal non-nilpotent groups (also ...
A 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 ...
Ballester Bolinches, Adolfo; Esteban Romero, Ramón(Cambridge University Press, 2003-10)
[EN] Characterisations of finite groups in which normality is a transitive relation are presented
in the paper. We also characterise the finite groups in which every subgroup is either
permutable or coincides with its ...
A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids its chief factors. Partial cover and avoidance property has turned out to be very useful ...
[EN] The aim of this paper is to characterise the classes of groups in which every subnormal subgroup is normal, permutable, or S-permutable by the embedding of the subgroups (respectively, subgroups of prime power order) ...
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.