  We obtain some results that answer certain questions of Lorenzini on wild
quotient singularities in dimension two. Using Kato's theory of log structures
and log regularity, we prove that the dual graph of exceptional curves on the
resolution of singularities contains at least one node. Furthermore, we show
that diagonal quotients for Hermitian curves by analogues of Heisenberg groups
lead to examples of wild quotient singularities where the dual graph contains
at least two nodes.
