Published online by Cambridge University Press: 20 November 2018
A finite group is said to have deficiency zero if it can be presented with an equal number of generators and relations. Finite metacyclic groups of deficiency zero have been classified, see  or . Finite non-metacyclic groups of deficiency zero, which we denote by FD 0-groups, are relatively scarce. In  I. D. Macdonald introduced a class of nilpotent FD 0-groups all having nilpotent class≤8. The largest nilpotent class known for a Macdonald group is 7 . Only a finite number of nilpotent FD 0-groups, other than the Macdonald groups, seem to be known , . In this note we exhibit a class of FD 0-groups which contains nilpotent groups of arbitrarily large nilpotent class.