Central factors of deficiency zero groups

Abstract

We answer a question of some twenty years standing: are the central factors of nilpotent groups of deficiency zero 3-generated? We prove that the answer is negative by giving an explicit presentation for a 3-generator, 3-relator group of order 2¹⁷ and class 5 which has central factors wl ch are 4-generated but not 3-generated. We outline the computatio al techniques which lead to this result.