Dear Experts,

1) Does someone know of any evaluation of the number of $p$-groups of order $p^n$ and rank $k$ ? (In particular, rank $2$? )

2) In the profinite group theory- we take a finitely generated free group $F$ , and denote by $S_f$ the interesection of all the normal subgroups $S \triangleleft F$ such that $F/S$ is a finite group. Does the group $F/S_f$ have a name? (It arises when talking about profinite completions, so I guessed it must have a name)

thanks a lot for any help ! Karrol