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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

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