Geodesic
Parallelisms of PG(n, q)
Mathematics and Education in Mathematics, Tome 51 (2022), pp. 113-123 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

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Let PG(n, q) be the n-dimensional projective space over the finite field GF(q). A set of lines, such that each point is in exactly one of these lines, is called a spread. A parallelism is a partition of the lines of the projective space to spreads. The present paper considers the main properties of parallelisms of PG(n, q), the motivation for their study, the known results and some open problems in this research area. Нека PG(n, q) е n-мерното проективно пространство над крайното поле GF(q). Множество от прави на PG(n, q) такива, че всяка точка се съдържа точно в една от тях, се нарича спред. Паралелизъм наричаме множество от спредове, за което е в сила, че всяка права на PG(n, q) се съдържа в точно един негов спред. Настоящата статия се спира на свойствата на паралелизмите на PG(n, q), на причините за интереса към тях, на резултатите, получени в тази област, и на някои отворени въпроси.
Keywords: Projective space, parallelism, classification, automorphism, 05B25, 05B40, 05E20, Projective space, parallelism, classification, automorphism, 05B25, 05B40, 05E20 
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     author = {Topalova, Svetlana and Stela, Zhelezova},
     title = {Parallelisms of {PG(n,} q)},
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Topalova, Svetlana; Stela, Zhelezova. Parallelisms of PG(n, q). Mathematics and Education in Mathematics, Tome 51 (2022), pp. 113-123. http://geodesic.mathdoc.fr/item/MEM_2022_51_a8/