# Locality and Centrality: The Variety ZG

@article{Amarilli2021LocalityAC, title={Locality and Centrality: The Variety ZG}, author={Antoine Amarilli and Charles Paperman}, journal={ArXiv}, year={2021}, volume={abs/2102.07724} }

We study the variety ZG of monoids where the elements that belong to a group are central, i.e., commute with all other elements. We show that ZG is local, that is, the semidirect product ZG ∗ D of ZG by definite semigroups is equal to LZG, the variety of semigroups where all local monoids are in ZG. Our main result is thus: ZG ∗ D = LZG. We prove this result using Straubing’s delay theorem, by considering paths in the category of idempotents. In the process, we obtain the characterization ZG…

## One Citation

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