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Non-amalgamation of ordered groups

Published online by Cambridge University Press:  24 October 2008

A. M. W. Glass ,
D. Saracino  and
C. Wood
A. M. W. Glass
Affiliation:
Bowling Green State University, Bowling Green, OH 43403
D. Saracino
Affiliation:
Colgate University, Hamilton, NY 13346
C. Wood
Affiliation:
Wesleyan University, Middletown, CT 06457
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Extract

An ordered group (o-group for short) is a group endowed with a linear (i.e. total) order such that for all x, y, z, xz ≤ yz and zx ≤ zy whenever x ≤ y. A group for which such an order exists is called an orderable group. A group G is said to be divisible if for each positive integer m and each g ε G, there is x ε G such that xm = g.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 2 , March 1984 , pp. 191 - 195
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

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