EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 98(112), pp. 31–44 (2015)

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On commutativity of quasi-minimal groups

Slavko Moconja

Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

Abstract: We investigate if every quasi-minimal group is abelian, and give a positive answer for a quasi-minimal pure group having a $\emptyset$-definable partial order with uncountable chains. We also relate two properties of a complete theory in a countable language: the existence of a quasi-minimal model and the existence of a strongly regular type. As a consequence we derive the equivalence of conjectures on commutativity of quasi-minimal groups and commutativity of regular groups.

Keywords: quasi-minimal group; strongly regular type

Classification (MSC2000): 03C45; 03C60; 20A15

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Electronic fulltext finalized on: 18 Nov 2015. This page was last modified: 6 Jan 2016.

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