title: 2-Supernilpotent Mal'cev algebras.
abstract: In this note we prove that a Mal'cev algebra is 2-supernilpotent ([1, 1, 1] =  0) if and only if it is polynomially equivalent to a special expanded group. This generalizes Gumm's result that a Mal'cev algebra is abelian if and only if it is polynomially equivalent to a module over a ring.
authors: Institut für Algebra, Johannes Kepler Universität, 4040  Linz, Austria ; Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, 21000  Novi Sad, Serbia.
authors: Nebojša
authors: N
authors: Mudrinski
keywords: Commutators; Expanded group; Mal’cev algebra; Nilpotent