On a class of groups with Lagrangian factor groups.
On finite minimal non-p-supersoluble groups
If ℱ is a class of groups, then a minimal non-ℱ-group (a dual minimal non-ℱ-group resp.) is a group which is not in ℱ but any of its proper subgroups (factor groups resp.) is in ℱ. In many problems of classification of groups it is sometimes useful to know structure properties of classes of minimal non-ℱ-groups and dual minimal non-ℱ-groups. In fact, the literature on group theory contains many results directed to classify some of the most remarkable among the aforesaid classes. In particular, V....
On finite soluble groups verifying an extremal condition on subgroups.
We classify the finite soluble groups satisfying the following condition: if H is a subgroup of G and H is not nilpotent, then the Fitting subgroup of H is the centralizer in H of its derived subgroup H'.
Su una classe di gruppi ipercentrali
In this paper we prove a theorem which extends a result due to H. Heineken. We prove that if ( hypercentral not locally cyclic p-group with property (P) in no. 1, hypercentral group) then is a hypercentral p-group. More generally: if (G hypercentral torsion group, soluble group) then is a locally finite group.
Page 1