  A wired tree is a graph obtained from a tree by collapsing the leaves to a
single vertex. We describe a pair of short exact sequences relating the
sandpile group of a wired tree to the sandpile groups of its principal
subtrees. In the case of a regular tree these sequences split, enabling us to
compute the full decomposition of the sandpile group as a product of cyclic
groups. This resolves in the affirmative a conjecture of E. Toumpakari
concerning the ranks of the Sylow p-subgroups.
