Published online by Cambridge University Press: 20 November 2018
For unimodular semidirect products of locally compact amenable groups $N$ and
$H$, we show that one can always construct a Følner net of the form
$({{A}_{\alpha }}\,\times \,{{B}_{\beta }})$
for
$G$, where
$({{A}_{\alpha }})$
is a strong form of Følner net for
$N$ and
$({{B}_{\beta }})$
is any Følner net for
$H$. Applications to the Heisenberg and Euclidean motion groups are provided.