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

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Priming Construction IIUsing the FKS examples as a starting point, we get elusive groupsfor all degreesp2 n r j 11 . . . r tjtwhere• p Mersenne,• 2 n > p,• r 1 , . . . , r t are distinct odd primes dividing p − 1,• j i ≥ 0.Using Hensel lifting construction can also multiply by powers of p.
A characterisationTheorem (MG-Kelly 2008+)Let G be an elusive permutation group such that G = N ⋊ G 1 forN an elementary abelian minimal normal subgroup and G 1 cyclic.Then G can be obtained by repeatedly applying the primingconstruction to an FKS-group.
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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 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: Priming Construction IIUsing the FK
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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