12.24 (1992)

Given a ring $R$ with identity, the automorphisms of $R[[x]]$ sending $x$ to $x(1 + \sum_{i=1}^\infty a_i x^i)$, $a_i \in R$, form a group $N(R)$. We know that $N(\mathbb{Z})$ contains a copy of the free group $F_2$ of rank 2 and, from work of A. Weiss, that $N(\mathbb{Z}/p\mathbb{Z})$ contains a copy of every finite $p$-group (but not of $\mathbb{Z}_{p^\infty}$), $p$ a prime. Does $N(\mathbb{Z}/p\mathbb{Z})$ contain a copy of $F_2$?