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] The solubility of a finite group with less than 6 non-supersoluble subgroups is confirmed in the paper. Moreover we prove that a finite insoluble group has exactly 6 non-supersoluble subgroups if and only if it is ...

[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 ...

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.