Characterization of class groups of Krull monoids via their systems of sets of lengths: a status report

Abstract. This paper gives an overview of results on the systems of sets of lengths of Krull monoids, with a focus on monoids with finite class group where each class contains a prime divisor. There is an emphasis on results that allow to characterize (properties of) the class group via the system of sets of lengths. Moreover, it is shown for some further groups that the system of sets of lengths characterizes the class group. 1