7 problems

Class-group determination conjecture. The system $\mathcal L(H)$ determines the class group $G$, apart from the two trivial exceptions given in Theorem A.

Characteristic systems-of-sets-of-lengths conjecture. The system of sets of lengths is characteristic for the group: if finite abelian groups $G$ and $G'$ have the same system of s…

Let $H$ and $H'$ be transfer Krull monoids with weak transfer homomorphisms to monoids of product-one sequences over finite abelian groups $G$ and $G'$, respectively. Their systems…

Characterization conjecture. If

Let $H$ be a Krull monoid with finite class group $G$, and let … be its system of sets of lengths, where $\mathsf L(a)$ is the set of factorization lengths of $a$. The system…

Characteristic system of sets of lengths conjecture. The system $\mathcal L(H)$ is characteristic for the class group: conversely, it determines $G$ up to isomorphism.

Let $H$ be a Krull monoid as in Theorem 5.3, with associated set $G_P$, and suppose in addition that … For $k\in\mathbb N$, let $\mathcal U_k(H)$ denote the union of the sets of le…