For the dimension of the Cartan subgroup, see Rank of a Lie group

In the mathematical subject of group theory, the rank of a group G, denoted rank(G), can refer to the smallest cardinality of a generating set for G, that is

If G is a finitely generated group, then the rank of G is a nonnegative integer. The notion of rank of a group is a group-theoretic analog of the notion of dimension of a vector space. Indeed, for p-groups, the rank of the group P is the dimension of the vector space P/Φ(P), where Φ(P) is the Frattini subgroup.