Groups and plane geometry (Q817696)
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scientific article; zbMATH DE number 5013032
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Groups and plane geometry |
scientific article; zbMATH DE number 5013032 |
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Groups and plane geometry (English)
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17 March 2006
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In the precisely written paper the author shows that the first-order theory of a large class of plane geometries and the first-order theory of their groups of motions, understood both as groups with a unary predicate singling out line-reflections and as groups acting on sets, are mutually interpretable. The paper was inspired by some talks with J. Diller and shows interesting connexions with papers of D. Lascar, R. S. Millman, K. Prazmowski, A. Prusinska and W. Szczerba.
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Erlanger Programm
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mutually interpretable theories
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groups generated by involutions
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group actions
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line reflections
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metric planes
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