The inverse Erdos-Heilbronn Problem for restricted set addition in finite groups

We provide a survey of results concerning both the direct and inverse problems to the Cauchy-Davenport theorem and Erdos-Heilbronn problem in Additive Combinatorics. We prove a slight extension to an inverse theorem of Dias da Silva-Hamidoune in Z/pZ, and we present a counterexample to an open conjecture concerning the inverse Erdos-Heilbronn problem in nonabelian groups.