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

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The answer is that there should be no such simple group. Questions of this kind belong to a project in which Alex has been a leading force: Recognition of finite simple groups by the properties of a single element. To recognize an almost simple permutation group by a single element becomes feasible due to the O’Nan Scott Theorem: If G is maximal, not containing Alt n , with G ⊂ Sym n then G belongs to one of 5 well-understood classes, or otherwise, is almost simple.
Therefore, given g ∈ Sym n with regular orbits, can we identify the primitive almost simple groups G with 〈 g 〉 ⊂ G ⊂ Sym n The problem I first mentioned is a key step towards answering such questions. I will report about joint work with Alex Zalesskii.
Page 1 and 2: Permutation representations of fini
Page 3 and 4: Let n ≥ k be integers, k not a pr
Page 5: The answer is that there should be
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 and 28: Proposition: Let G be doubly transi
Page 29 and 30: 2. Intersections of conjugacy class
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

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

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