Abstract
We study the problem concerning the influence of the index of maximal subgroup or the degree of primitive permutation representation of the finite simple groups on the structure of a group. Let G be a finite group and s be the index of maximal subgroup of the Monster M. In this paper, we prove that there exists an epimorphism from G to M or A s if G has the primitive permutation representation of degree s, and as a consequence we prove that the Monster is determined by every s.
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