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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 someof what is known and not yet known about the minimum sizes of these three typesof sumsets, as well as their corresponding critical numbers. In particular, wediscuss several new open direct and inverse problems.

Open problems about sumsets in finite abelian groups: minimum sizes and critical numbers