  Given a regular subgroup R of AGL_n(F), one can ask if R contains nontrivial
translations. A negative answer to this question was given by Liebeck, Praeger
and Saxl for AGL_2(p) (p a prime), AGL_3(p) (p odd) and for AGL_4(2). A
positive answer was given by Hegedus for AGL_n(p) when n >= 4 if p is odd and
for n=3 or n >= 5 if p=2. A first generalization to finite fields of Hegedus'
construction was recently obtained by Catino, Colazzo and Stefanelli. In this
paper we give examples of such subgroups in AGL_n(F) for any n >= 5 and any
field F. For n < 5 we provide necessary and sufficient conditions for their
existence, assuming R to be unipotent if char F=0.
