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Advances in Geometry

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Classification of 8-dimensional rank two commutative semifields

Michel Lavrauw / Morgan Rodgers
Published Online: 2018-03-26 | DOI: https://doi.org/10.1515/advgeom-2017-0064

Abstract

We classify the rank two commutative semifields which are 8-dimensional over their center ūĚĒĹq. This is done using computational methods utilizing the connection to linear sets in PG(2, q4). We then apply our methods to complete the classification of rank two commutative semifields which are 10-dimensional over ūĚĒĹ3. The implications of these results are detailed for other geometric structures such as semifield flocks, ovoids of parabolic quadrics, and eggs.

Keywords: Semifield; commutative semifield; flocks; linear sets

MSC 2010: 51E20; 12K10

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About the article


Received: 2016-05-09

Revised: 2016-11-04

Published Online: 2018-03-26


Funding: The authors acknowledge funding from the research project ‚ÄúFinite Geometry with Applications in Algebra and Combinatorics‚ÄĚ, funded by the Dipartimento di Tecnica e Gestione dei Sistemi Industriali of the Universit√° di Padova.


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0064.

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