The localglobal property for Ginvariant terms
Abstract
For some Maltsev conditions $\Sigma$ it is enough to check if a finite algebra $\mathbf A$ satisfies $\Sigma$ locally on subsets of bounded size, in order to decide, whether $\mathbf A$ satisfies $\Sigma$ (globally). This localglobal property is the main known source of tractability results for deciding Maltsev conditions. In this paper we investigate the localglobal property for the existence of a $G$term, i.e. an $n$ary term that is invariant under permuting its variables according to a permutation group $G \leq$ Sym($n$). Our results imply in particular that all cyclic loop conditions (in the sense of Bodirsky, Starke, and Vucaj) have the localglobal property (and thus can be decided in polynomial time), while symmetric terms of arity $n>2$ fail to have it.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.02065
 Bibcode:
 2021arXiv210902065K
 Keywords:

 Mathematics  Rings and Algebras;
 Computer Science  Computational Complexity;
 03C05;
 08A70;
 20B05
 EPrint:
 22 pages