Resumen de On the upper central series of infinite groups

Maria De Falco, F. de Giovanni, Carmela Musella, Yaroslav P. Sysak

• Two relevant theorems by R. Baer and P. Hall show that a group is finite over a term with finite ordinal type of its upper central series if and only if it is finite-by-nilpotent. Extending these results, we prove here that if is any group, the hypercentre factor group is finite if and only if contains a finite normal subgroup such that is hypercentral (where the hypercentre of is defined as the last term of its upper central series).