  The Jacobian group (also known as the critical group or sandpile group) is an
important invariant of a finite, connected graph $X$; it is a finite abelian
group whose cardinality is equal to the number of spanning trees of $X$
(Kirchhoff's Matrix Tree Theorem). A specific type of covering graph, called a
derived graph, that is constructed from a voltage graph with voltage group $G$
is the object of interest in this paper. Towers of derived graphs are studied
by using aspects of classical Iwasawa Theory (from number theory). Formulas for
the orders of the Sylow $p$-subgroups of Jacobians in an infinite voltage
$p$-tower, for any prime $p$, are obtained in terms of classical $\mu$ and
$\lambda$ invariants by using the decomposition of a finitely generated module
over the Iwasawa Algebra.
