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

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2-closuresThe 2-closure G (2) of G is the group of all permutations of Ωwhich fix setwise each orbit of G on Ω × Ω.If G is 2-transitive on Ω then G (2) = Sym(Ω).G (2) preserves all systems of imprimitivity for G.We say that G is 2-closed if G = G (2) .The full automorphism group of a digraph is 2-closed.
Polycirculant conjectureKlin (1997) extended the question of Marušič to 2-closed groups.
Page 1 and 2: Fixed point free elements of prime
Page 6: How many?Let n = |Ω| > 1,G a trans
Page 9 and 10: How many? IIFulman-Guralnick (2003)
Page 11 and 12: What are they?Fein-Kantor-Schacher
Page 13: Elusive groupsWe say that a transit
Page 16 and 17: Elusive groupsWe say that a transit
Page 18 and 19: A question of MarušičMarušič (1
Page 20 and 21: A question of MarušičMarušič (1
Page 22 and 23: Nice representationsBiggs 197300 11
Page 24 and 25: 2-closuresThe 2-closure G (2) of G
Page 26 and 27: 2-closuresThe 2-closure G (2) of G
Page 30 and 31: Polycirculant conjectureKlin (1997)
Page 32 and 33: Early resultsMarušič (1981): All
Page 34 and 35: Early resultsMarušič (1981): All
Page 36: 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 and 90:
Page 91 and 92:
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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