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On primitive permutation groups with small suborbits and their orbital graphs
Li, Cai Heng ; Lu, Zai Ping ; Marušič, Dragan
Študiramo 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.
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