Corrigendum The number of generators of finite p-groups

Abstract

The author recently noted that the paper contains serious errors. Several classes of finite p-groups are defined, by requiring certain inequalities to hold between the numbers of generators of various subgroups. These requirements obviously go over to subgroups, but they need not go over to factor groups, a fact that was overlooked: we regarded all relevant classes as both subgroup and quotient closed. Here we note which results still hold, and o¤er substitutes for the other ones.The author is indebted to I. Snopce for pointing out that the results are problematic, and for providing the example of Demushkin groups, described below. Some of the results were announced in [3], and, unfortunately, the incorrect results were applied in at least one case, in [2, Lemma 14], whose proof is therefore invalid. This does not seem to a¤ect any other proof in [2].Two types of inequalities are considered, additive and multiplicative. The first one gives rise to classes A k , defined as follows.