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 ...
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] 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 ...
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 ...
[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] 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, 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 ...