Permutation representations of finite simple groups: Orbits of cyclic ...

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2. Intersections of conjugacy classes: Let G be in L1, acting doubly transitively on Ω and ω ∈ Ω. Let C = 〈 g 〉 be cyclic, square-free without loss. One needs to show that for some a ∈ G. C ∩ (G ω ) a = 1
2. Intersections of conjugacy classes: Let G be in L1, acting doubly transitively on Ω and ω ∈ Ω. Let C = 〈 g 〉 be cyclic, square-free without loss. One needs to show that for some a ∈ G. C ∩ (G ω ) a = 1 This requires case by case analysis. In the linear situation induction over the number of Jordan blocks of g on the underlying vector space can be used. Similar comments apply to the factorization case. This completes the list L1. The groups in L2 all have rank 3 actions. However, as yet this can not be used. So also here intersection type arguments are needed. Technically quite involved!
Page 1 and 2: Permutation representations of fini
Page 3 and 4: Let n ≥ k be integers, k not a pr
Page 5 and 6: The answer is that there should be
Page 7 and 8: Therefore, given g ∈ Sym n with r
Page 9 and 10: For cyclic C let the square-free pa
Page 11 and 12: [2] : Let (G, Ω) be an action of t
Page 13 and 14: It is a special case of a Theorem o
Page 15 and 16: The key observation is therefore th
Page 17 and 18: Main Theorem Let G be an almost sim
Page 19 and 20: L2: G is a classical group, not alr
Page 21 and 22: It is expected that the theorem hol
Page 23 and 24: Idea of the Proof A mixture of the
Page 25 and 26: Proposition: Let G be doubly transi
Page 27: Proposition: Let G be doubly transi
Page 31 and 32: Embeddings Comment 1: As an example
Page 33 and 34: Embeddings Comment 1: As an example
Page 35 and 36: Comment 2: Moving on from cyclic su
Page 37 and 38: Comment 2: Moving on from cyclic su
Page 39 and 40: Here the lemma for permutation modu
Page 41 and 42: Proof: Let G 1 , .., G t be a syste
Page 43: Proof: Let G 1 , .., G t be a syste

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