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

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Some more affine examples• V = GF(7 3 ), W a 2-dimensional subspace, G 1 = 3 1+2 ⋊ Q 8 ,H 1 = 3 2 ⋊ C 2 . (CGJKLMN 2002)• p a Mersenne <strong>prime</strong>, V = GF(2) p2 −1 , W a hyperplane,G 1 = AΓL(1, p 2 ), H 1 = (C p ⋊ C p−1 ) × C 2 . (MG 2007)• V = GF(2) 8 , W a codimension 2 space,G 1 = AΓL(1, 9), H 1 = (C 3 ⋊ C 2 ) × C 2 . (MG 2007)
Hensel lifting constructionCameron-MG-Jones-Kantor-Klin-Marušič-Nowitz (2002)• V , G 1 , W <strong>and</strong> H 1 as in affine construction.• V dimension d over GF(p).• W dimension k.
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 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: Some more affine examples• V = GF
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 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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