A bad group is a group of finite Morley rank which is non-solvable, but has the property that every proper subgroup is nilpotent. Bad groups are conjectured to not exist. This would follow from the Cherlin-Zilber conjecture.

The original plan for proving the Cherlin-Zilber conjecture was to prove that bad groups and bad fields do not exist. However, bad fields were subsequently shown to exist. (A bad field is…a field of finite Morley rank such that has a definable proper subgroup?) ::: ::: :::