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Permutation representation of groups with Boolean orthogonalities

Part of: Ordered structures Connections with other structures, applications

Published online by Cambridge University Press:  09 April 2009

Gary Davis
Gary Davis
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria, 3083, Australia
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Abstract

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Reduced rings and lattice-ordered groups are examples of groups with Boolean orthogonalities. In this note we show that any group with a Boolean orthogonality satisfying a finiteness condition introduced by Stewart is isomorphic with a group of homeomorphisms of a topological space, in which two homeomorphisms are orthogonal if and only if they have disjoint supports.

MSC classification

Secondary: 54H10: Topological representations of algebraic systems 06F15: Ordered groups 54H15: Transformation groups and semigroups 57S99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 4 , April 1981 , pp. 412 - 418
Copyright
Copyright © Australian Mathematical Society 1981

References

Cornish, W. H. (1975), ‘Boolean orthogonalities and minimal prime subgroups’, Comm. Algebra 3, 859–900.Google Scholar
Cornish, W. H. and Stewart, P. N. (1977), ‘Direct and subdirect decompositions of universal algebras with a Boolean orthogonality’, preprint.Google Scholar
Davis, G. E. (1971a), Orthogonality relations on groups and rings (Ph. D. thesis, Monash University, Vic.).Google Scholar
Davis, G. E. (1971b), ‘Rings with orthogonality relations’, Bull. Austral. Math. Soc. 4, 163–178.Google Scholar
Davis, G. E. (1975), ‘Orthogonality relations on abelian groups’ J. Austral. Math. Soc. 19, 173–179.Google Scholar
Holland, C. (1963), ‘The lattice-ordered group of automorphisms of an ordered set’, Michigan Math. J. 10, 399–408.Google Scholar
Stewart, P. N. (1975), ‘A sheaf-theoretic representation of rings with a Boolean orthogonality’, Pacific J. Math. 58, 249–254.Google Scholar