On a general associativity law in groupoids (Q1207679)
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scientific article; zbMATH DE number 164935
| Language | Label | Description | Also known as |
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| English | On a general associativity law in groupoids |
scientific article; zbMATH DE number 164935 |
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On a general associativity law in groupoids (English)
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12 May 1993
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In the theory of nonassociative groupoids the main problem is to overcome the difficulties caused by the absence of the associativity law. In this paper we reduce calculations in a groupoid to calculations in a group. In order to do this certain transitivity properties of mappings on the groupoid are used. The main result is: if a general associativity law is satisfied in a division groupoid \(G\), then \(G\) is in fact a group.
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nonassociative groupoids
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associativity law
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division groupoid
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