Abelian and Non-Abelian Triangle Mysteries

Authors

Lon Mitchell, University of South Florida St. PetersburgFollow
Michael A. Jones
Brittany Shelton

SelectedWorks Author Profiles:

Lon Mitchell

Document Type

Article

Publication Date

2016

ISSN

0002-9890 (Print) 1930-0972 (Online)

Abstract

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.

Publisher

Taylor & Francis

Recommended Citation

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