Supernilpotent groups and 3-supernilpotent loops

Author:

Stanovský David1,Vojtěchovský Petr2

Affiliation:

1. Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Prague, Czech Republic

2. Department of Mathematics, University of Denver, 2390 S. York St., Denver, Colorado 80208, USA

Abstract

We find a short equational basis for the variety of [Formula: see text]-supernilpotent loops. We also present a conceptually simple proof that [Formula: see text]-nilpotence and [Formula: see text]-supernilpotence are equivalent for groups. Connections between [Formula: see text]-supernilpotent loops, Moufang loops, code loops, automorphic loops and AIM loops are explored.

Funder

Simons Foundation Mathematics and Physical Sciences Collaboration

PROF grant of the University of Denver

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Algebra and Number Theory

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