On a general associativity law in groupoids
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.
scientific article; zbMATH DE number 164935