English

On split extensions of preordered groups

Category Theory 2022-12-15 v1 Group Theory

Abstract

We investigate the behaviour of split extensions in the category OrdGrp of (pre)\-ordered groups. Namely we show that the lexicographic order plays a key role on the existence of compatible orders for semidirect products, establishing necessary and sufficient conditions for such existence; we prove that the Split Short Five Lemma holds for stably strong split extensions, and identify classes of split extensions which admit a classifier.

Keywords

Cite

@article{arxiv.2212.07064,
  title  = {On split extensions of preordered groups},
  author = {Maria Manuel Clementino and Carla Ruivo},
  journal= {arXiv preprint arXiv:2212.07064},
  year   = {2022}
}