C. E. Praeger and J. Saxl, On the orders of primitive permutation groups. Bull. Lond. Math. Soc. 37 (1980) 303--307.

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Reconstructing Simple Group Actions - Kantor, Penttila   (Correct)

....more instances of Hypothesis 2.1 occur; but the various views of this group are allowed in the proposition. Proof. Compare [Ka3] which uses the bound jGj n 8 based on [Ka1] and [LaS] instead of bounds in [Li] and [LiS] When G is an alternating group, bounds on the orders of subgroups [PS] yield (ii) Maz] takes care of the sporadic groups. In view of the classification of finite simple groups, it remains only to consider the groups of Lie type. Bounds on the degrees of permutation representations of exceptional groups of Lie type are given in [LiS] Those results imply that the ....

C. E. Praeger and J. Saxl, On the orders of primitive permutation groups. Bull. Lond. Math. Soc. 37 (1980) 303--307.

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