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

Autor:	Stela Zhelezova, Svetlana Topalova
Rok vydání:	2021
Předmět:	Combinatorics Set (abstract data type) Finite field Point set Projective space Order (ring theory) Partition (number theory) Invariant (mathematics) Automorphism Mathematics
Zdroj:	Computer Algebra in Scientific Computing ISBN: 9783030851644 CASC
DOI:	10.1007/978-3-030-85165-1_23
Popis:	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++.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::2884e2e21b5e1994b6163a01cda593bf https://doi.org/10.1007/978-3-030-85165-1_23 Zobrazit plný text záznamu