Group in which all minimal generating sets have the same size

Definition
Suppose $$G$$ is a defining ingredient::minimally generated group, i.e., it is a group with the property that it has a defining ingredient::minimal generating set (note that any finite group is minimally generated). We say that $$G$$ is a group in which all minimal generating sets have the same size if it is true that any two minimal generating sets of $$G$$ have the same size (i.e., the same cardinality).

Note that this same size must therefore be the minimum size of generating set, and must also be the maximum size of minimal generating set. In fact, an alternative definition is that the minimum size of generating set must equal the maximum size of minimal generating set.