  A. H. Rhemtulla proved that if a group is a residually finite p-group for
infinitely many primes p, then it is two-sided orderable. In problem 10.30 of
the Kourovka notebook 14th. edition, N. Ya. Medvedev asked if there is a
non-right-orderable group which is a residually finite p-group for at least two
different primes p. Using a result of Dave Witte, we will show that many
subgroups of finite index in GL_3(Z) give examples of such groups. On the other
hand we will show that no such example can exist among solvable by finite
groups.
