  We investigate the finite soluble groups $G$ with the following property
(replacement property): for every irredundant generating set
$\{g_1,\dots,g_m\}$ of maximal size and for any $1\neq g\in G$ there exists an
$i\in \{1,\dots,m\}$ so that $\langle
g_1,\dots,g_{i-1},g,g_{i+1},\dots,g_m\rangle=G.$
