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For $n\ge2$, let $F_n$ be the free group of rank $n$, and let $\IA(F_n)$ be the group of automorphisms of $F_n$ acting trivially on its abelianization. Two natural filtrations of $\IA(F_n)$ are its lower central series $\gamma_c(\IA(F_n))$ and the Andreadakis filtration $\mathrm{I}_{c+1}\mathrm{A}(F_n)$, consisting of...
Let $F_n$ be the free group of rank $n\geq2$ with basis $x_1,\ldots,x_n$. For $1\leq j<i\leq n$, let $d_{i,j}$ and $e_{i,j}$ be the automorphisms of $F_n$ defined by $d_{i,j}(x_i)=x_ix_j$ and $e_{i,j}(x_i)=x_jx_i$, respectively, and fixing the remaining free generators. Write $D_n=\langle d_{i,j}\mid 1\leq j<i\leq n\ra...
Let $F_n$ be a free group of rank $n\geq3$, freely generated by $x_1,\ldots,x_n$. For $1\leq j<i\leq n$, let $d_{i,j}$ denote the Nielsen automorphism of $F_n$ defined by $d_{i,j}(x_i)=x_ix_j$ and $d_{i,j}(x_k)=x_k$ for $k\neq i$, and let $D_n=\langle d_{i,j}\mid 1\leq j<i\leq n\rangle$. We determine the lower central...
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