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A characterization of lattice-ordered groups by their convex L-subgroups

Published online by Cambridge University Press:  09 April 2009

Paul Conrad
Affiliation:
The Australian National UniversityCanberra
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In this paper we show that whether or not a group admits a lattice-order often depends upon whether or not it possesses a set of subgroups that satisfy certain algebraic conditions. Using these techniques we are able to determine large classes of groups that can be lattice-ordered.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Byrd, R., Tulane Thesis 1966.Google Scholar
[2]Conrad, P., Harvey, J. and Holland, C., ‘The Hahn embedding theorem for abelian lattice-ordered groups’, Trans. Amer. Math. Soc. 108 (1963), 143169.CrossRefGoogle Scholar
[3]Conrad, P., ‘Embedding theorems for abelian groups with valuations’, Amer. J. Math. 75 (1953), 129.CrossRefGoogle Scholar
[4]Conrad, P., ‘The lattice of all convex l-subgroups of a lattice-ordered group’, Czech. Math. J. 15 (1965), 101123.Google Scholar
[5]Fuchs, L., Partially ordered algebraic systems (Pergamon Press, 1963).Google Scholar
[6]Iwasawa, K., ‘On linearly ordered groups’, J. Math. Soc. Japan 1 (1948), 19.Google Scholar
[7]Malcev, A., ‘On ordered groups’, Izvestiya Akad. Nauk SSSR. Ser. Mat. 13 (1949), 473482.Google Scholar
[8]Neumann, B. H., ‘On ordered groups’, Amer. J. Math. 71 (1949) 118.CrossRefGoogle Scholar
[9]Podderyugin, V., ‘A condition of orderability for a group’. Izvestiya Akad. Nauk. SSSR. Ser. Mat. 21 (1957), 199208.Google Scholar
[10]Rieger, L., 'On the ordered and cyclically ordered groups I, II, III, Vestnik Kralovske Ceske Spolecnosti Nauk (1946) 131, (1947) 1–33, (1948) 1–26.Google Scholar