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New Parallelisms of \(\mathrm{PG}(3,5)\) with Automorphisms of Order 8

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Computer Algebra in Scientific Computing (CASC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12865))

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Abstract

Let \(\mathrm{PG}(n,q)\) be the n-dimensional projective space over the finite field \({\mathbb F}_q\). A spread in \(\mathrm{PG}(n,q)\) is a set of lines which partition the point set. A partition of the lines of the projective space by spreads is called a parallelism. The study of parallelisms is motivated by their numerous relations and applications. We construct 8958 new nonisomorphic parallelisms of \(\mathrm{PG}(3,5)\). They are invariant under cyclic automorphism groups of order 8. Some of their interesting properties are discussed. We use the system for computational discrete algebra GAP as well as our own MPI-based software written in C++.

The authors acknowledge the provided access to the e-infrastructure of the NCHDC – part of the Bulgarian National Roadmap on RIs, with the financial support by the Grant No D01-221/03.12.2018.

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Acknowledgments

The authors are grateful to the anonymous referees for the very careful reading of the paper, and for their adequate remarks and suggestions on the presentation of the material.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetlana Topalova & Stela Zhelezova

Authors
  1. Svetlana Topalova
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  2. Stela Zhelezova
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Correspondence to Stela Zhelezova .

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Editors and Affiliations

  1. Université de Lille, Villeneuve d’Ascq, France

    François Boulier

  2. Coventry University, Coventry, UK

    Matthew England

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Topalova, S., Zhelezova, S. (2021). New Parallelisms of \(\mathrm{PG}(3,5)\) with Automorphisms of Order 8. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2021. Lecture Notes in Computer Science(), vol 12865. Springer, Cham. https://doi.org/10.1007/978-3-030-85165-1_23

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  • DOI: https://doi.org/10.1007/978-3-030-85165-1_23

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  • Online ISBN: 978-3-030-85165-1

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