Geodesic
Generalized Torsion Elements and Bi-orderability of 3-manifold Groups
Canadian mathematical bulletin, Tome 60 (2017) no. 4, pp. 830-844

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DOI

It is known that a bi-orderable group has no generalized torsion element, but the converse does not hold in general. We conjecture that the converse holds for the fundamental groups of 3-manifolds and verify the conjecture for non-hyperbolic, geometric 3-manifolds. We also confirm the conjecture for some infinite families of closed hyperbolic 3-manifolds. In the course of the proof, we prove that each standard generator of the Fibonacci group $F(2,m)\,(m>2)$ is a generalized torsion element.
DOI : 10.4153/CMB-2017-008-8
Mots-clés : 57M25, 57M05, 06F15, 20F05, generalized torsion element, bi-ordering, h-manifold group 
Motegi, Kimihiko; Teragaito, Masakazu. Generalized Torsion Elements and Bi-orderability of 3-manifold Groups. Canadian mathematical bulletin, Tome 60 (2017) no. 4, pp. 830-844. doi: 10.4153/CMB-2017-008-8
@article{10_4153_CMB_2017_008_8,
     author = {Motegi, Kimihiko and Teragaito, Masakazu},
     title = {Generalized {Torsion} {Elements} and {Bi-orderability} of 3-manifold {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {830--844},
     year = {2017},
     volume = {60},
     number = {4},
     doi = {10.4153/CMB-2017-008-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-008-8/}
}
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