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

More documents

Recommendations

Info

L2: G is a classical group, not already listed in L1: • Symplectic groups PSp(2n, q), • Unitary groups PSU(n, q), • Orthogonal groups O(2n + 1, q), O + (2n, q), O − (2n, q). Let L be the union of L1 and L2 but remove any group whose socle is an alternating group. A group in L acts non-trivially on the set ∆ if its socle is not the identity group on ∆. Theorem (Emmett, Siemons & Zalesski, 2000, ’02, ’10): Let G be in L and suppose that G acts non-trivially on the set ∆. Then every cyclic subgroup of G has a regular orbit on ∆.
It is expected that the theorem holds more generally for all almost simple groups with socle not equal to an alternating group.
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: L2: G is a classical group, not alr
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 ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?