---- > [!definition] Definition. ([[perfect group]]) > A [[group]] $G$ is called a **perfect group** if the [[commutator subgroup]] $[G,G]$ equals $G$ itself. > [!basicexample] > A sufficient but not necessary condition to be a [[perfect group]] is to be [[abelian group|nonabelian]] and [[simple group|simple]]. ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```