Classification

Lemma 12.1.1. Let X = A+Zp~na be a crq-group where A G Regg(X), a G A, and \X/A\ = pn. Assume that β* < pn for every critical type τ of X . If B is another regulating subgroup of X such that X /B is cyclic, then X = B + Zp~na and a G B.