Let $G$ be a finite group. Denote by $D(G)$ the maximal size of a minimal generating set, (minimal in the sense of inclusion). I vaguely remember seeing recently something on $D(G)$. Can anyone refer me to anything new or old? 



Maximal size of minimal generating set
The maximum size of minimal generating sets of a finite group is studied recently by Lucchini in the following two papers:


Andrea Lucchini, [The largest size of a minimal generating set of a finite group](http://dx.doi.org/10.1007/s00013-013-0527-y), *Arch. Math. (Basel)* **101**(1) (2013), 1–8.


Andrea Lucchini, [Minimal generating sets of maximal size in finite monolithic groups](http://dx.doi.org/10.1007/s00013-013-0583-3), *Arch. Math. (Basel)* **101**(5) (2013), 401–410.


