Base sizes for simple groups and a conjecture of Cameron
TC Burness, MW Liebeck… - Proceedings of the London …, 2009 - Wiley Online Library
Proceedings of the London Mathematical Society, 2009•Wiley Online Library
Let G be a permutation group on a finite set Ω. A base for G is a subset B⊆ Ω with pointwise
stabilizer in G that is trivial; we write b (G) for the smallest size of a base for G. In this paper
we prove that b (G)⩽ 6 if G is an almost simple group of exceptional Lie type and Ω is a
primitive faithful G‐set. An important consequence of this result, when combined with other
recent work, is that b (G)⩽ 7 for any almost simple group G in a non‐standard action, proving
a conjecture of Cameron. The proof is probabilistic and uses bounds on fixed point ratios.
stabilizer in G that is trivial; we write b (G) for the smallest size of a base for G. In this paper
we prove that b (G)⩽ 6 if G is an almost simple group of exceptional Lie type and Ω is a
primitive faithful G‐set. An important consequence of this result, when combined with other
recent work, is that b (G)⩽ 7 for any almost simple group G in a non‐standard action, proving
a conjecture of Cameron. The proof is probabilistic and uses bounds on fixed point ratios.
Let G be a permutation group on a finite set Ω. A base for G is a subset B ⊆ Ω with pointwise stabilizer in G that is trivial; we write b(G) for the smallest size of a base for G. In this paper we prove that b(G) ⩽ 6 if G is an almost simple group of exceptional Lie type and Ω is a primitive faithful G‐set. An important consequence of this result, when combined with other recent work, is that b(G) ⩽ 7 for any almost simple group G in a non‐standard action, proving a conjecture of Cameron. The proof is probabilistic and uses bounds on fixed point ratios.
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