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

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The key observation is therefore that the cyclic C of order k has an orbit of length k = |C| if and only if the module for a primitive k th root of unity appears in F Ω. Our version of the Burnside-Brauer Lemma is
The key observation is therefore that the cyclic C of order k has an orbit of length k = |C| if and only if the module for a primitive k th root of unity appears in F Ω. Our version of the Burnside-Brauer Lemma is Lemma (Siemons & Zalesski, 2002): Let C be a cyclic permutation group on Ω. Then the number of regular orbits of C on Ω is the multiplicity of the regular module F C in F Ω.
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: It is a special case of a Theorem o
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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