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.
* The variety generated by a finite group has a finite number of nonisomorphic critical groups.

## External links[edit]

* Definition of critical group

This abstract algebra-related article is a stub. You can help Wikipedia by expanding it.

|

* v
* t
* e

*[v]: View this template
*[t]: Discuss this template
*[e]: Edit this template