  We prove that Abels' group over an arbitrary nondiscrete locally compact
field has a quadratic Dehn function. As applications, we exhibit connected Lie
groups and polycyclic groups whose asymptotic cones have uncountable abelian
fundamental group. We also obtain, from the case of finite characteristic,
uncountably many non-quasi-isometric finitely generated solvable groups, as
well as peculiar examples of fundamental groups of asymptotic cones.
