Left Orderable Residually Finite p-groups

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.