Desarguesian spreads and field reduction for elements of the semilinear group
- Author
- Geertrui Van de Voorde (UGent)
- Organization
- Abstract
- The goal of this note is to create a sound framework for the interplay between field reduction for finite projective spaces, the general semilinear groups acting on the defining vector spaces and the projective semilinear groups. This approach makes it possible to reprove a result of Dye on the stabiliser in PGL of a Desarguesian spread in a more elementary way, and extend it to P Gamma L(n, q). Moreover a result of Drudge [5] relating Singer cycles with Desarguesian spreads, as well as a result on subspreads (by Sheekey, Rottey and Van de Voorde [18]) are reproven in a similar elementary way. Finally, we try to use this approach to shed a light on Condition (A) of Csajbok and Zanella, introduced in the study of linear sets [4]. (C) 2016 Elsevier Inc. All rights reserved.
- Keywords
- POLAR SPACES, BOSE REPRESENTATION, M-SYSTEMS, ANDRE/BRUCK, Field reduction, Desarguesian spread
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8507283
- MLA
- Van de Voorde, Geertrui. “Desarguesian Spreads and Field Reduction for Elements of the Semilinear Group.” LINEAR ALGEBRA AND ITS APPLICATIONS, vol. 507, 2016, pp. 96–120, doi:10.1016/j.laa.2016.05.038.
- APA
- Van de Voorde, G. (2016). Desarguesian spreads and field reduction for elements of the semilinear group. LINEAR ALGEBRA AND ITS APPLICATIONS, 507, 96–120. https://doi.org/10.1016/j.laa.2016.05.038
- Chicago author-date
- Van de Voorde, Geertrui. 2016. “Desarguesian Spreads and Field Reduction for Elements of the Semilinear Group.” LINEAR ALGEBRA AND ITS APPLICATIONS 507: 96–120. https://doi.org/10.1016/j.laa.2016.05.038.
- Chicago author-date (all authors)
- Van de Voorde, Geertrui. 2016. “Desarguesian Spreads and Field Reduction for Elements of the Semilinear Group.” LINEAR ALGEBRA AND ITS APPLICATIONS 507: 96–120. doi:10.1016/j.laa.2016.05.038.
- Vancouver
- 1.Van de Voorde G. Desarguesian spreads and field reduction for elements of the semilinear group. LINEAR ALGEBRA AND ITS APPLICATIONS. 2016;507:96–120.
- IEEE
- [1]G. Van de Voorde, “Desarguesian spreads and field reduction for elements of the semilinear group,” LINEAR ALGEBRA AND ITS APPLICATIONS, vol. 507, pp. 96–120, 2016.
@article{8507283,
abstract = {{The goal of this note is to create a sound framework for the interplay between field reduction for finite projective spaces, the general semilinear groups acting on the defining vector spaces and the projective semilinear groups. This approach makes it possible to reprove a result of Dye on the stabiliser in PGL of a Desarguesian spread in a more elementary way, and extend it to P Gamma L(n, q). Moreover a result of Drudge [5] relating Singer cycles with Desarguesian spreads, as well as a result on subspreads (by Sheekey, Rottey and Van de Voorde [18]) are reproven in a similar elementary way. Finally, we try to use this approach to shed a light on Condition (A) of Csajbok and Zanella, introduced in the study of linear sets [4]. (C) 2016 Elsevier Inc. All rights reserved.}},
author = {{Van de Voorde, Geertrui}},
issn = {{0024-3795}},
journal = {{LINEAR ALGEBRA AND ITS APPLICATIONS}},
keywords = {{POLAR SPACES,BOSE REPRESENTATION,M-SYSTEMS,ANDRE/BRUCK,Field reduction,Desarguesian spread}},
language = {{eng}},
pages = {{96--120}},
title = {{Desarguesian spreads and field reduction for elements of the semilinear group}},
url = {{http://doi.org/10.1016/j.laa.2016.05.038}},
volume = {{507}},
year = {{2016}},
}
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