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

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Locally quasiprimitive graphs IITheorem (Praeger 1985)Let Γ be a finite connected G-vertex-transitive,G-locally-quasiprimitive graph <strong>and</strong> let 1 ≠ N ⊳ G. If N has atleast three vertex-orbits then it is semiregular.
Locally quasiprimitive graphs IITheorem (Praeger 1985)Let Γ be a finite connected G-vertex-transitive,G-locally-quasiprimitive graph <strong>and</strong> let 1 ≠ N ⊳ G. If N has atleast three vertex-orbits then it is semiregular.CorollaryEither G contains a semiregular subgroup, or G is quasiprimitive orbiquasiprimitive on vertices.
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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
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 28 and 29: 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 75 and 76: Locally quasiprimitive graphsΓ a g
Page 77: Locally quasiprimitive graphsΓ a g
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 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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