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Apr 17, 2016 at 20:20 comment added HJRW It's a standard fact (I should of course have said all torsion-free one-relator groups are left-orderable). The only proof I know is to use the ideas of arXiv:1410.2540 to prove that they're locally indicable, and then to quote the well known theorem that locally indicable groups are left-orderable.
Apr 17, 2016 at 20:01 vote accept Shahrooz
Apr 17, 2016 at 19:42 history edited Stefan Kohl CC BY-SA 3.0
Amended answer.
Apr 17, 2016 at 17:34 comment added Shahrooz Dear HJRW, I saw it after some search in google. But, would you please introduce me some good reference about the proof of this fact and some related similar theorems?
Apr 17, 2016 at 13:01 comment added HJRW All one-relator groups are left-orderable.
Apr 17, 2016 at 9:37 comment added Shahrooz Thanks dear Kohl, is there any method such that we can check in GAP that the group $G$ is orderable?
Apr 17, 2016 at 9:32 history answered Stefan Kohl CC BY-SA 3.0