... class of group extensions that includes each of the groups We conjecture subgroup and quotient group properties of these extensions ON THE GALOIS GROUPS OF THE 2-CLASS FIELD TOWERS OF SOME IMAGINARY ... ABSTRACT Title of dissertation: ON THE GALOIS GROUPS OF THE 2-CLASS FIELD TOWERS OF SOME IMAGINARY QUADRATIC FIELDS Aliza Steurer, Doctor of Philosophy, 2006 Dissertation directed by: Professor Lawrence ... show that the groups in L5 are terminal Among the collection of groups on L1 , , L5 , there are 12 candidates, each having exponent-2 class Therefore, G must be one of these 12 groups In particular,...