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Let p and q be distinct primes, and G an elementary amenable group that is a residually
finite p-group and a residually finite q-group. We conjecture that such groups G are left
orderable. In this paper we show some results which came as attempts to prove this conjecture. In particular we give a condition under which split extensions of residually finite
p-groups are again residually finite p-groups. We also give an example which shows that
even for elementary amenable groups, it is not sufficient for biorderablity that the group be
a residually finite p-group and a residually finite q-group.