Groupes dont le centralisateur d'un sous-groupe est d'ordre borné.
Groups in which the bounded nilpotency of two-generator subgroups is a transitive relation.
Groups of Order which is Indivisible by a Fixed Prime
Groups saturated by a finite set of groups.
Groups whose all subgroups are ascendant or self-normalizing
This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972,...
Groups with every subgroup ascendant-by-finite
A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.
Groups with many nearly normal subgroups
Un sottogruppo di un gruppo si dice nearly normal se ha indice finito nella sua chiusura normale . In questa nota si caratterizzano i gruppi in cui ogni sottogruppo che non sia nearly normal soddisfa una fissata condizione finitaria per diverse scelte naturali della proprietà .
Groups with metamodular subgroup lattice
A group G is called metamodular if for each subgroup H of G either the subgroup lattice 𝔏(H) is modular or H is a modular element of the lattice 𝔏(G). Metamodular groups appear as the natural lattice analogues of groups in which every non-abelian subgroup is normal; these latter groups have been studied by Romalis and Sesekin, and here their results are extended to metamodular groups.
Groups with nearly modular subgroup lattice
A subgroup H of a group G is nearly normal if it has finite index in its normal closure . A relevant theorem of B. H. Neumann states that groups in which every subgroup is nearly normal are precisely those with finite commutator subgroup. We shall say that a subgroup H of a group G is nearly modular if H has finite index in a modular element of the lattice of subgroups of G. Thus nearly modular subgroups are the natural lattice-theoretic translation of nearly normal subgroups. In this article we...
Groups with subnormal subgroups of bounded defect
Gruppi con pochi sottogruppi non quasinormali