Realizable Dicyclic Groups

It is well-known that the units of a ring forms a group called the group of units. A group that is the group of units for some ring is said to be realizable. Fuchs’ problem asks whether a given group is realizable by some ring. In this paper, we present the resolution of Fuchs’ problem for dihedral groups as given in [CL1]. We then present partial results for dicyclic groups. For dicyclic groups of order 12 and smaller, our results are complete