On commutativity of quasi-minimal groups | Zendy

Slavko Moconja | Zendy

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On commutativity of quasi-minimal groups

Author(s) -

Slavko Moconja

Publication year - 2015

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim150510030m

Subject(s) - abelian group , mathematics , commutative property , uncountable set , countable set , group (periodic table) , equivalence (formal languages) , pure mathematics , order (exchange) , discrete mathematics , physics , quantum mechanics , finance , economics

We investigate if every quasi-minimal group is abelian, and give a positive answer for a quasi-minimal pure group having a ∅-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.

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