  Boyer, Gordon, and Watson have conjectured that an irreducible rational
homology 3-sphere is an L-space if and only if its fundamental group is not
left-orderable. Since Dehn surgeries on knots in $S^3$ can produce large
families of L-spaces, it is natural to examine the conjecture on these
3-manifolds. Greene, Lewallen, and Vafaee have proved that all 1-bridge braids
are L-space knots. In this paper, we consider three families of 1-bridge
braids. First we calculate the knot groups and peripheral subgroups. We then
verify the conjecture on the three cases by applying the criterion developed by
Christianson, Goluboff, Hamann, and Varadaraj, when they verified the same
conjecture for certain twisted torus knots and generalized the criteria of Clay
and Watson and of Ichihara and Temma.
