On the Fitting length of
For a finite group , the intersection graph of which is denoted by is an undirected graph such that its vertices are all nontrivial proper subgroups of and two distinct vertices and are adjacent when . In this paper we classify all finite groups whose intersection graphs are regular. Also, we find some results on the intersection graphs of simple groups and finally we study the structure of .
Gli autori studiano il sottogruppo intersezione dei sottogruppi massimali e non supersolubili di un gruppo finito e le relazioni tra la struttura di e quella di .
In this paper, the structures of collection of pronormal subgroups of dicyclic, symmetric and alternating groups are studied in respect of formation of lattices and sublattices of . It is proved that the collections of all pronormal subgroups of and S do not form sublattices of respective and , whereas the collection of all pronormal subgroups of a dicyclic group is a sublattice of . Furthermore, it is shown that and ) are lower semimodular lattices.