A noncommutative ordinally simple linearly ordered group
A. H. Clifford · Proceedings of the American Mathematical Society · 1951
B. H. Neumann' has recently given an example of a noncommutative ordinally simple linearly ordered group.2 This confirmed a conjecture of Garrett Birkhoff3 that there must exist ordinally simple ordered groups which are not merely subgroups of the additive group of real numbers. In the present note we give a more elementary example. Let G be the group generated by a set of symbols g(a), one to each rational number ax, subject to the generating relations