In the middle of the 19th century Cauchy and Liouville proved theorems describing the behavior of certain harmonic functions in Euclidean space.

We will discuss the "proper" definitions of these notions in the setting of discrete groups.  These include how to define which functions are "polynomials" and which are "harmonic" on an abstract group.

We will prove a theorem relating these notions, which is the analog of Liouville's theorem in the classical case.

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