Abstract
For a positive integer h and a subset A of a given finite abelian group, we let hA, \(h \hat{\;} A\), and \(h_{\pm }A\) denote the h-fold sumset, restricted sumset, and signed sumset of A, respectively. Here we review some of what is known and not yet known about the minimum sizes of these three types of sumsets, as well as their corresponding critical numbers. In particular, we discuss several new open direct and inverse problems.
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