Abelian and Non-Abelian Triangle Mysteries
0002-9890 (Print) 1930-0972 (Online)
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.
Taylor & Francis
Mitchell, L., Jones, M. A., & Shelton, B. (2016) Abelian and Non-Abelian Triangle Mysteries. The American Mathematical Monthly, 123(8), 808-813. https://doi.org/10.4169/amer.math.monthly.123.08.808