Stopnja lihosti tranzitivnih permutacijskih grup / Oddness degree of transitive permutation groups (OddGroups)
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Naziv Tittle |
Stopnja lihosti tranzitivnih permutacijskih grup / Oddness degree of transitive permutation groups (OddGroups) |
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Akronim Acronim |
N1-0062 |
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Opis Description |
(SI) Raziskovalni problem OddGroups projekta: Določi, katere izmed naštetih treh možnosti, veljajo za dano grupo H. Primeri vseh izmed treh možnosti obstajajo. Alternirajoča grupa A5 kot grupa, ki deluje na Petersenovem grafu, je soda in liho-zaprta. Grupa PSL(2,17) kot grupa, ki deluje na kubičnem ločno-tranzitivnem grafu reda 102, je soda in nično-liha. Obstajajo pa tudi primeri sodih grup, ki so orbitalno-lihe; celo grupe s sodim 2-zaprtjem, za katere ima vsak orbitalni (di)graf lihe avtomorfizme. Tak primer je grupa SL(2,16) stopnje 51, ki deluje na prostoru odsekov po podgrupi reda 80, iz katere izhajata dva izomorfna razreda bazičnih orbitalnih (di)grafov (Fermatov graf in unija 17ih usmerjenih 3-ciklov). (EN) The Core OddGroups Research Problem is: Determine which of these three possibilities, occurs for H. Examples of each of the three possibilities exist. The group A5 acting on the Petersen graph is even and closure-odd. The group PSL(2,17) acting on the unique cubic arc-transitive graph of order 102 is even and zero-odd. There are also examples of even groups which are orbital-odd; in fact, groups with even 2-closures for which every orbital (di)graph has odd automorphisms. Such is the case with SL(2,16) of degree 51 acting on the coset space of a subgroup of order 80 and giving rise to basic orbital (di)graphs of two isomorphism classes (a Fermat graph and a union of 17 directed 3-cycles). |
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Vrsta projekta Project Type |
Projekti medn. sodelovanja |
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Trajanje Duration |
01/06/2017 - 30/05/2020 |
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URL URL |
https://p1-0285.iam.upr.si/sl/projekti/n1-0062 |
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Vodja projekta Project Leader |
Dragan Marušič |
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Sodelujoče organizacije Participating organizations |
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Oddelek Department |
Oddelek za matematiko IAM |