444 KB54 KB200820252021Skresanov, Saveliy V.številka:1letnik:21str. 105-124DOI:10.26493/1855-3974.2450.1dcCOBISSID_HOST:111656451ISSN:1855-3966URN:URN:NBN:SI:doc-W7852IQJenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporanea2-closure2-zaprtjegraf ranga 3grupa ranga 3permutacijska grupapermutation grouprank 3 graphrank 3 groupOn 2-closures of rank 3 groups|A permutation group ?$G$? on ?$\Omega$? is called a rank 3 group if it has precisely three orbits in its induced action on ?$\Omega \times \Omega$?. The largest permutation group on ?$\Omega$? having the same orbits as ?$G$? on ?$\Omega \times \Omega$? is called the 2-closure of ?$G$? A description of 2-closures of rank 3 groups is given. As a special case, it is proved that the 2-closure of a primitive one-dimensional affine rank 3 group of sufficiently large degree is also affine and one-dimensionalPermutacijska grupa ?$G$? na ?$\Omega$? se imenuje grupa ranga 3, če ima njeno inducirano delovanje na ?$\Omega \times \Omega$? natančno tri orbite. Največja permutacijska grupa na, ki ima iste orbite kot ?$G$? na ?$\Omega \times \Omega$?, se imenuje 2-zaprtje grupe ?$G$. Predstavimo opis 2-zaprtij gr?up ranga 3. Kot poseben primer dokažemo, da je 2-zaprtje primitivne enodimenzionalne afine grupe ranga 3 dovolj velikega reda prav tako afino in enodimenzionalnoTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije