descriptionPublicationkeyboard_double_arrow_right Article , Preprint 17 May 2023Embargo end date: 01 Jan 2022Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Portugaliae Mathematica, volume 80, pages 327-341 (issn: 0032-5155, eissn: 1662-2758,

Authors: Maria Manuel Clementino; Carla Ruivo;

doi: 10.4171/pm/2101 , 10.48550/arxiv.2212.07064

arXiv: http://arxiv.org/abs/2212.07064

handle: 10316/114074

On split extensions of preordered groups

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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.

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Keywords

FOS: Mathematics, Mathematics - Category Theory, Category Theory (math.CT), Group Theory (math.GR), 06F15, 18E13, 08C05, Mathematics - Group Theory

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