Bad group

Origin
The term bad group was introduced by Gregory Cherlin, as an example of groups that should not exist. They are groups that provide very strong counterexamples to the Cherlin conjecture.

Symbol-free definition
A group (possibly with additional structure and relations) is termed a bad group if it is connected, not solvable, has finite Morely rank, and in which every definable proper subgroup is nilpotent-by-finite. It is conjectured that bad groups do not exist.