Groups with Locally Modular Homogeneous Pregeometries are Commutative

Groups with Locally Modular Homogeneous Pregeometries are Commutative

It is well known that strongly minimal groups are commutative. Whether this is true for various generalisations of strong minimality has been asked in several different settings (see Hyttinen [2002], Maesono [2007], Pillay and Tanovi\'c [2011]). In this note we show that the answer is positive...

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1. Verfasser: Haykazyan, Levon
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
Mathematics - Group Theory
Mathematics - Logic
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Zusammenfassung:It is well known that strongly minimal groups are commutative. Whether this is true for various generalisations of strong minimality has been asked in several different settings (see Hyttinen [2002], Maesono [2007], Pillay and Tanovi\'c [2011]). In this note we show that the answer is positive for groups with locally modular homogeneous pregeometries.
DOI:10.48550/arxiv.1702.06043