Centralisers of Formal Maps

We consider the formal maps in any finite dimension d with coefficients an integral domain K identity. Those invertible under composition form a group [inline-graphic 1i]. centraliser Cg of element g ∈ 1i] infinite order, tangent to identity If has order and is field characteristic zero, we show that contains isomorphic copy additive (K, +). positive characteristic, uncountable abelian subgroup. The proofs are quite different but connected by so-called sum functions.