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

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It is a special case of a Theorem of Burnside, we will come back to this later. Example: Look at two elements of order 6. First take g = (1, 2)(3, 4, 5)(6). It has eigenvalues λ i , µ j and ν satisfying λ 2 i = µ 3 j = ν = 1. Correspondingly, F Ω = 3I 1 + I 2 + I 3 + I 4 .
It is a special case of a Theorem of Burnside, we will come back to this later. Example: Look at two elements of order 6. First take g = (1, 2)(3, 4, 5)(6). It has eigenvalues λ i , µ j and ν satisfying λ 2 i = µ 3 j = ν = 1. Correspondingly, F Ω = 3I 1 + I 2 + I 3 + I 4 . On the other hand, if g = (1, 2, 3, 4, 5, 6) then its eigenvalues are the 6 distinct roots of unity and F Ω = I 1 + I 2 + I 3 + I 4 + I 5 + I 6 .
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: [2] : Let (G, Ω) be an action of t
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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