References
- Bludov , V. V. 1972 . An example of an unordered group with strictly isolated identity element . Algebra i Logika , 1 : 341 – 349 .
- Bludov , V. V. , Glass , A. M. W. and Rhemtulla , A. 2003 . Ordered groups in which all convex jumps are central . J. Korean Math. Soc. , 40 : 225 – 239 .
- Glass , A. M. W. 1999 . Partially Ordered Groups , Series in Algebra Vol. 7 , London : World Scientific .
- Hall , P. 1963 . On non-strictly simple groups . Proc. Camb. Phil. Soc. , 59 : 531 – 553 .
- Johnson , D. L. 1988 . The group of formal power series under substitution . J. Austral. Math. Soc. (Series A) , 45 : 296 – 302 .
- Kokorin , A. I. and Kopitov , V. M. 1974 . Fully Ordered Groups New York : John Wiley & Sons .
- Kopitov , V. M. 1998 . Groups of formal power series are fully orderable . Algebra and Logic , 37 : 170 – 180 . (Translated from Algebra i Logika (1998),37: 301–309)
- Kopitov , V. M. and Medvedev , N. Ya. 1996 . Right-Ordered Groups New York : Plenum Publishing Corporation .
- Kropholler , P. H. 1984 . On finitely generated soluble groups with no large wreath product sections . Proc. London Math. Soc. , 49 : 155 – 169 .
- Mura , R. and Rhemtulla , A. 1977 . Orderable Groups , Lecture Notes in Pure and Applied Mathematics Vol. 27 , New York : Marcel Dekker .
- Ohnishi , M. 1950 . On linearization of ordered groups . Osaka J. Math. , 2 : 161 – 164 .
- aThe answer is no. In a paper by Bludov,Glass and Rhemtulla ([2003]) an example of a finitely generated orderable metabelian group G is constructed. This group is residually torsion-free nilpotent but not of finite rank. G/C is nilpotent for every normal non-trivial relatively convex subgroup C of G. It follows from these properties that G is an R + group.