Section of a rooted-tree automorphism
= Section of a rooted-tree automorphism
For an automorphism $g$ of a regular rooted tree and a first-level vertex $i$, the section $g_i$ is the induced automorphism of the rooted subtree at $i$, defined by
$$
g(iv)=g(i)g_i(v).
$$
An automorphism fixing the first level is determined by the tuple of all its sections.