Abstract Let 𝐺 be a permutation group, with minimal degree μ (G) (G) and base size b (G) b (G). We show that there exists a universal constant c > 0 c>0 such that, for infinitely many 𝑛, there is a transitive permutation group 𝐺 of degree 𝑛 with μ (G) b (G) ≥ c ⋅ n 2 (G) b (G) c n^2. We also identify some classes of transitive and intransitive groups whose base size and minimal degree have a smaller upper bound, shared with primitive groups.
Guerra et al. (Tue,) studied this question.
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