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}
}