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All current techniques for showing that a number field has an infinitep-class field tower depend on one of various forms of the Golod-Shafarevichinequality. Such techniques can also be used to restrict the types of p-groupswhich can occur as Galois groups of finite p-class field towers. In the casethat the base field is a quadratic imaginary number field, the theoryculminates in showing that a finite such group must be of one of three possiblepresentation types. By keeping track of the error terms arising in standardproofs of Golod-Shafarevich type inequalities, we prove a Golod-Shafarevichequality for analytic pro-p-groups. As an application, we further work ofSkopin, showing that groups of the third of the three types mentioned above arenecessarily tremendously large.

A Golod-Shafarevich Equality and p-Tower Groups