Abelian and Non-Abelian Triangle Mysteries
Lon H. Mitchell, Michael A. Jones, Brittany C. Shelton · Digital Commons - University of South Florida (University of South Florida) · 2016
Behrends and Humble characterized the Abelian groups behind mysterious behavior related to certain triangular arrays and asked if such triangles could be constructed from non-Abelian groups. We show that commutativity plays an essential role in quasigroup and semigroup triangle mysteries and prove that “mysterious groups” must be Abelian.