| Let A be a commutative local ring with maximal ideal M. In this dissertation we will discuss the normal subgroups of the general linear group GL(2, A). In [3], Costa and Keller define large normal subgroups of GL(2, A) called generic groups and prove that a subgroup N of GL(2, A) is normal if and only if N is contained in a generic group and N contains the commutator subgroup of the generic group with GL(2, A). With the aid of the radix theory introduced and developed in [4] and [5], we give an explicit description of all generic groups and their commutator subgroups. This breaks down into cases depending on the form of the residue field A/M. We also give a result that links the work of Lacroix [7] to the theory of radices. |
