Critical group

In mathematics, in the realm of group theory, a group is said to be critical if it is not in the variety generated by all its proper subquotients, which includes all its subgroups and all its quotients.


 * Any finite monolithic A-group is critical. This result is due to Kovacs and Newman. But not every monolithic group is critical.
 * The variety generated by a finite group has a finite number of nonisomorphic critical groups.