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On primitive permutation groups with small suborbits and their orbital graphsLi, Cai Heng ; Lu, Zai Ping ; Marušič, DraganŠtudiramo primitivne grupe z malimi podorbitami. Z uporabo klasifikacijskih rezultatov Quirina [Math. Z. 122 (1971) 267] in Wanga [Comm. Algebra 20 (1992) 889] je določena natančna lista vseh ... primitivnih grup s podorbitami dolžine 4. Pokažemo, da ne obstaja nobena taka grupa s točkovnim stabilizatorjem reda ▫$2^4 \cdot 3^6$▫, s čimer rešimo odprto vprašanje iz 70-tih let. Podana je tudi analiza orbitalnih grafov primitivnih permutacijskih grup s podorbitami dolžine 3 oziroma 4. Dobljena je popolna klasifikacija ločno tranzitivnih grafov s primitivno grupo avtomorfizmov valence 3 in 4. Pokažemo, da ne obstaja noben ločno tranzitiven graf valence manj kot 10 s primitivno grupo avtomorfizmov. Podana je tudi konstrukcija poltranzitivnih grafov valence ▫$2k$▫, za neskončno mnogo ▫$k \ge 7$▫ s primitivno grupo avtomorfizmov.Source: Journal of algebra. - ISSN 0021-8693 (Vol. 279, no. 2, 2004, str. 749-770)Type of material - article, component partPublish date - 2004Language - englishCOBISS.SI-ID - 13161049
Author
Li, Cai Heng |
Lu, Zai Ping |
Marušič, Dragan
Topics
algebra |
teorija grafov |
permutacijska grupa |
primitivna grupa |
podorbita |
graf |
ločno tranzitiven graf |
poltranzitiven graf |
algebra |
graph theory |
permutation group |
primitive group |
suborbit |
graph |
arc-transitive graph |
half-arc-transitive graph
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Li, Cai Heng | ![]() |
Lu, Zai Ping | ![]() |
Marušič, Dragan | 02887 |
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