Computation of a Unit Index

Abstract

This chapter is due to Kersey. We determine the index of the group of Klein units in the group of all units in case the conductor is the power of a prime ideal pⁿ. For the composite case, we refer to [Ke 2]. The treatment differs from, say, Robert’s [Ro 1] in several ways. First we deal with the somewhat larger group of Klein units rather than Robert units; and second, we introduce intermediate groups other than those of Robert, more in line with the Sinnott computation of the index in the composite case for cyclo-tomic fields.