Fixed point free elements of prime order - School of Maths and Stats ...

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Open problems and questions• Prove the polycirculant conjecture.• Prove the polycirculant conjecture for arc-transitive graphs.• Find new constructions of elusive groups.• For what degrees do elusive groups exist? (smallest degree forwhich existence is unknown is 40.)
Open problems and questions• Prove the polycirculant conjecture.• Prove the polycirculant conjecture for arc-transitive graphs.• Find new constructions of elusive groups.• For what degrees do elusive groups exist? (smallest degree forwhich existence is unknown is 40.)• Does the set of all such degrees have density 0?
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Fixed point free elements of prime
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How many?Let n = |Ω| > 1,G a trans
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How many? IIFulman-Guralnick (2003)
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What are they?Fein-Kantor-Schacher
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Elusive groupsWe say that a transit
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Elusive groupsWe say that a transit
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A question of MarušičMarušič (1
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A question of MarušičMarušič (1
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Nice representationsBiggs 197300 11
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2-closuresThe 2-closure G (2) of G
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Page 28 and 29:
Page 30 and 31:
Polycirculant conjectureKlin (1997)
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Early resultsMarušič (1981): All
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Early resultsMarušič (1981): All
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Fein-Kantor-Schacher examplesAGL(1,
Page 41 and 42: More constructionsCameron-MG-Jones-
Page 43 and 44: General affine constructionCameron-
Page 45 and 46: FKS examples againAGL(1, p 2 ) ∼
Page 53 and 54: Some more affine examples• V = GF
Page 55 and 56: Hensel lifting constructionCameron-
Page 57 and 58: Hensel lifting constructionCameron-
Page 59 and 60: Priming ConstructionMG 2007Input:
Page 61 and 62: Priming Construction IIUsing the FK
Page 63 and 64: A characterisationTheorem (MG-Kelly
Page 65 and 66: Primitive groups and generalisation
Page 67 and 68: ClassificationsTheorem (MG 2003)The
Page 69 and 70: ClassificationsTheorem (MG 2003)The
Page 71 and 72: Classifications IITheorem (MG-Xu 20
Page 73 and 74: Locally quasiprimitive graphsΓ a g
Page 79 and 80: Locally quasiprimitive graphs IIThe
Page 81 and 82: Locally quasiprimitive graphs IIITh
Page 83 and 84: Some more resultsDobson-Malnič-Mar
Page 85 and 86: Some more resultsDobson-Malnič-Mar
Page 87 and 88: Open problems and questions• Prov
Page 89: Open problems and questions• Prov
Page 93: Group Theory, Combinatorics and Com
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Fixed point free elements of prime order - School of Maths and Stats ...

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