On Commutativity and Groupoid Identities between Products with 3 Factors
Tjark Weber · 2009
A groupoid consists of a set G equipped with a binary operation. This article examines the relationship between commutativity and various (less common) groupoid identities between products with 3 factors, e.g., (xy)z =( yz)x. We systematically study all 12 identities of this form to identify additional conditions (e.g., unitality) that are sufficient for commutativity. Automated deduction techniques were used in several parts of the work.