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Relations, homogeneity and group quotients

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

M. W. Warner
M. W. Warner
Affiliation:
Department of Mathematics, The City University, Northampton Square, London ECI, United Kingdom
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Abstract

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A set with a relation is isomorphic to a group quotient under the condition described as weak homogeneity, and to the quotient of a group with relation preserved by right and left translations if the homogeneity is strengthened. A method of constructing these group quotients and, furthermore, all such very homogeneous spaces, is described and an illustrative example given.

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 3 , February 1981 , pp. 347 - 355
Copyright
Copyright © Australian Mathematical Society 1981

References

Arbib, M. A., ‘Tolerance automata’, Kybernetika (Prague) 3, 223–233.Google Scholar
Muir, A. and Warner, M. W. (1979), ‘Tolerability, tolerance and automata’, Research Memorandum 12, Department of Mathematics, The City University, London.Google Scholar
Muir, A. and Warner, M. W. (1980), ‘Homogeneous tolerance spaces’, Czechoslovak Math. J. 30 (105), 47–55.CrossRefGoogle Scholar