Magma Automorphisms and Quasi-Linear Cycle Sets

Abstract

Rump asked in 2016 whether every finite quasi-linear cycle set is retractible. We reinterpret this question in terms of automorphisms of certain pointed magmas, and propose a conjecture on the automorphisms of these magmas which would imply an affirmative answer to Rump's question. We provide some theoretical and computational evidence in support of our conjecture.