8.12 (1982)

Let $D_0$ denote the class of finite groups of deficiency zero, i. e. having a presentation $\langle X \mid R \rangle$ with $|X| = |R|$.
$\qquad$ a) Does $D_0$ contain any 3-generator $p$-group for $p \geqslant 5$?
$\qquad$ b) Are the central factors of nilpotent $D_0$-groups 3-generated?
$\qquad$ c) Do soluble $D_0$-groups have bounded derived length?
$\qquad$ d) Which non-abelian simple groups can occur as composition factors of $D_0$-groups?