  We consider formal maps in any finite dimension $d$ with coefficients in an
integral domain $K$ with identity. Those invertible under formal composition
form a group $\mathcal{G}$. We consider the centraliser $C_g$ of an element
$g\in\mathcal{G}$ which is tangent to the identity of $\mathcal{G}$. Elements
of finite order always have an uncountable centraliser. If $g$ has infinite
order and $K$ is a field of characteristic zero we show that $C_g$ contains an
isomorphic copy of the additive group $(K,+)$. If $g$ has infinite order and
$K$ has finite characteristic we show that $C_g$ contains an uncountable
abelian subgroup.
  The proofs are quite different in finite characteristic and in characteristic
zero, but are connected by so-called sum functions.
