Abstract
Our purpose is to show how the logic of relations can be uitilized in the study of group theory. There are some striking similarities in certain theorems in group theory and certain results about equivalence relations, and we show how the former can be derived as consequences of the latter. This transition is accomplished by means of certain ismorphism theorems, proved in considerable generality in section 2, and applied to groups in section 3. In section 1 we give several miscellaneous theorems on equivalence relations, which later turn out to have their analogues in the theory of groups.
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© 2001 Springer Science+Business Media Dordrecht
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Smullyan, R. (2001). Equivalence Relations and Groups. In: Anderson, C.A., Zelëny, M. (eds) Logic, Meaning and Computation. Synthese Library, vol 305. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0526-5_11
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DOI: https://doi.org/10.1007/978-94-010-0526-5_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3891-1
Online ISBN: 978-94-010-0526-5
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