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A Class of Right-Orderable Groups

Published online by Cambridge University Press:  20 November 2018

R. T. Botto Mura  and
A. H. Rhemtulla
R. T. Botto Mura
Affiliation:
University of Alberta, Edmonton, Alberta
A. H. Rhemtulla
Affiliation:
University of Alberta, Edmonton, Alberta
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Abstract

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A group g is called right-orderable (or an ro-group) if there exists an order relation ≦ on g such that a ≦ b implies ac ≦ be for all a, b, c in g. this is equivalent to the existence of a subsemigroup p of g such that p ⋂ p-1 = ﹛e﹜ and p ⋃ p-1 = g. given the order relation ≦, p can be taken to be the set of positive elements and conversely, given p, define a ≦ b if and only if ba-1ϵ p. a group g together with a given right-order relation on g is called right-ordered.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 3 , 01 June 1977 , pp. 648 - 654
Copyright
Copyright © Canadian Mathematical Society 1977

References

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5. Robinson, D. J. S., Infinite soluble and nilpotent groups, Queen Mary College Mathematics Notes (1967).Google Scholar