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On multilattice groups

Published online by Cambridge University Press:  24 October 2008

D. B. McAlister
D. B. McAlister
Affiliation:
Queen's University, Belfast
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Extract

Multilattice groups have been introduced by Benado ((1)) and considered by Vaida ((9)), who has initiated the study of the structure of a class of these groups. The purpose of this paper is to further the investigation begun by Vaida.

Basic in the work contained here is the set H consisting of the differences between the minimal upper bounds of pairs of elements of a multilattice group G. By means of conditions imposed on G and based on H, we determine the structure of the congruence relations on a multilattice group and study direct sums and lexicographic products and extensions of such groups (sections 2, 3).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 3 , July 1965 , pp. 621 - 638
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

REFERENCES

(1)Benado, M.Sur la théorie de la divisibilité. Acad. R.P. Romîne. Bul. Sti. Sect. Sti. Mat. -Fiz. 6, no. 2 (1954), 263–270.Google Scholar
(2)Benado, M.Les ensembles partiellement ordonnées et le théorème de raffinement de Schreier, II. Czechoslovak Math. J. (5) 80 (1955), 308–344.CrossRefGoogle Scholar
(3)Benado, M.Bemerkungen zur Theorie der Vielverbande, IV. Proc. Cambridge Philos. Soc. 56 (1960), 291–317.CrossRefGoogle Scholar
(4)Burgess, D. C. J.Generalized intervals in partially ordered groups. Proc. Cambridge Philos. Soc. 55 (1959), 165–171.CrossRefGoogle Scholar
(5)Conrad, P.Some structure theorems for lattice groups. Trans. American Math. Soc. 99 (1961), 212–240.CrossRefGoogle Scholar
(6)Fuchs, L.Partially ordered algebraic systems (Pergamon Press; London, 1963).Google Scholar
(7)Jaffard, P.Contribution a l'étude des groupes ordonnées. J. Math. Pures Appl. 32 (1953), 203–280.Google Scholar
(8)Teh, H. H.A note on l-groups. Proc. Edinburgh Math. Soc. 13 (Series II), Part I (1962), 123–24.CrossRefGoogle Scholar
(9)Vaida, D.Groupes ordonnées dont les éléments admettent une décomposition jordanienne généralisée. C.R. Acad. Sci. Paris, 257 (1963), 2053–55.Google Scholar