  In the study of the local dynamics of a germ of diffeomorphism fixing the
origin in C, an important problem is to determine the centralizer of the germ
in the group Diff(C,0) of germs of diffeomorphisms fixing the origin. When the
germ is not of finite order, then the centralizer is abelian, and hence a
maximal abelian subgroup of Diff(C,0). Conversely any maximal abelian subgroup
which contains an element of infinite order is equal to the centralizer of that
element. A natural question is whether every maximal abelian subgroup contains
an element of infinite order, or whether there exist maximal abelian torsion
subgroups; we show that such subgroups do indeed exist, and moreover that any
infinite subgroup of the rationals modulo the integers Q/Z can be embedded into
Diff(C,0) as such a subgroup.
