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

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Some more resultsDobson-Malnič-Marušič-Nowitz (2007):• All quartic vertex-transitive graphs have a fixed point freeautomorphism of prime order.• All vertex-transitive graphs of valency p + 1 admitting atransitive {2, p}-group for p odd have a fixed point freeautomorphism of prime order.
Some more resultsDobson-Malnič-Marušič-Nowitz (2007):• All quartic vertex-transitive graphs have a fixed point freeautomorphism of prime order.• All vertex-transitive graphs of valency p + 1 admitting atransitive {2, p}-group for p odd have a fixed point freeautomorphism of prime order.• There are no elusive 2-closed groups of square-free degree.
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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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Polycirculant conjectureKlin (1997)
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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: Some more resultsDobson-Malnič-Mar
Page 87 and 88: 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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