  We use a semigroup-theoretic construction by Peter Higgins in order to
produce, for each even $n$, an $n$-state and 3-letter synchronizing automaton
with the following two features: 1) all its input letters act as idempotent
selfmaps of rank $\dfrac{n}2$; 2) its reset threshold is asymptotically equal
to $\dfrac{n^2}2$.
  In the revised version a few inaccuracies (spotted by the anonymous referees
of the previous version) have been removed and several relevant references have
been added.
