On the Finite Group with the Index of Maximal Subgroups of the Monster

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.

Key Words:

• Finite simple group
• Maximal subgroup
• Index

Mathematics Subject Classification:

• 20D05
• 20B15

Acknowledgments

Li was supported by the NSF of Jiangsu Province and Jiangsu Province Colleges and Universities (Grant No. BK2001133, 03KJB110112).

Notes

^#Communicated by A. Olshanskii.