# Rank of a group

A notion from group theory. A group $G$ has finite general rank $r$ if $r$ is the minimal number such that any finitely-generated subgroup of $G$ is contained in a subgroup having $r'$ generators $(r'\leq r)$. A group $G$ has finite special rank $r$ if $r$ is the minimal number such that any finitely-generated subgroup of $G$ has a system of generators of at most $r$ elements. If no such finite number exists, then the general (special) rank of the group is said to be infinite.