The classification conjecture for unit reducible cyclotomic fields

Let $K_N=\mathbb{Q}(\zeta_N)$ be the cyclotomic field of conductor $N$, where $\zeta_N$ is a primitive $N$th root of unity. A cyclotomic field is unit reducible if it has the unit-reducibility property defined in the paper. The authors' conjecture. The cyclotomic fields $K_N$ where $N=3,4,5,7,8,9,11,12,15,20,21,24$ are the only unit reducible cyclotomic fields. Determining the complete list of unit reducible cyclotomic fields is the principal open problem identified by the authors; the paper establishes that only finitely many such fields exist but does not determine the entire list.